To eliminate y from the first equation, we can multiply the entire equation by -2. This will give us:
-2x - 4y = -12
Now, if we add this equation to the second equation, the y terms will cancel out, leaving us with:
-2x - 4(2) + 5z = 26
-2x + 5z = 26
Now we have two equations in two variables, x and z. We can solve this system of equations by substituting the value of y from the second equation into the first equation. This gives us:
x + 2(2) = -6
x = -10
Substituting this value of x into the second equation, we get:
-2(-10) + 5z = 26
20 + 5z = 26
5z = 6
z = 1.2
Finally, we can substitute the values of x and z back into the second equation to find the value of y:
-2(-10) - 6(1.2) + 5(1.2) = 26
20 - 7.2 + 6 = 26
12.8 = 26
This system of equations has no solution, since we have found values of x and z that make the second equation true, but substituting these values into the first equation results in a false statement. This means that there is no set of values for x, y, and z that will make all three equations true at the same time.
Some values of f(x, y) are given below. Write out the terms of a Riemann Sum (using four squares) that gives an upper estimate of r 4 0 r 4 0 f dx dy.
To find a Riemann sum that gives an upper estimate of the double integral, we need to divide the region of integration into small subregions (in this case, squares) and take the maximum value of f(x, y) over each subregion.
The Riemann sum will then be the sum of the areas of the subregions times the maximum value of f(x, y) over each subregion.
For example, if we divide the region of integration into four squares, the Riemann sum would be given by:
Riemann sum = (area of first square) * (maximum value of f(x, y) in first
square) + (area of second square) * (maximum value of
f(x, y) in second square) + (area of third square) *
(maximum value of f(x, y) in third square) + (area of fourth
square) * (maximum value of f(x, y) in fourth square)
We can then fill in the specific values of the areas and maximum values of f(x, y) for each square based on the given values of f(x, y).
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Image below to be answered
a.The formula that describe the sequence or progression is a+(7-7n)
b. 2nd term = -10 , 3rd term = 10, 4th term = -10 and 5th term = 10
What is arithmetic and geometric progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio.
Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
The nth term of an arithmetic progression is given as a(n)= a + (n − 1) × d
In geometric progression the nth term is given as a(n)= ar^(n-1)
where a is the first term
therefore if a = 12 and d is - 7
the formula for the arithmetic progression =
a(n) = 12+(n-1) -7 = 12+( 7-7n)
If the first term of a GP is 10 with common ratio of -1
then the second term = 10×-1 = -10
third term = -10×-1 = 10
fourth term = 10×-1 = -10
fifth term = -10× -1 = 10
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Draw a line segment with a length of 3 1/2 and a midpoint of -1.
The line segment of length 3 1/2 is sketched with mid pint at -1 and attached
What is a line segment?A line segment in geometry has two different points on it that define its boundaries.
A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
How to make the line segmentThe endpoints is important before a line can be defined as a line segment, however the midpoint will be essential in calculating for the endpoints
The mid point of the line is given to be -1
the other ends will be 3 1/2 /2
1.75
from -1 add and subtract 1.75 to get the endpoint's
-1 + 1.75 = 0.75
-1 - 1.75 = 2.75
each unit on the number line is 0.3333
to get 0.75 from 0 count two units to give 0.6667 then a bit more to get to 0.75
to get 2.75 from 2 count two strokes to get to 2.6667, then add a little more to get 2.75
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Please show work thank you
Rational functions
Division followed by simplification of mentioned rational function gives:
(x + 1)/(x + 4)
What is factorization?Factoring an algebraic expression specifically means writing a given expression as the product of its factors. These factors may be numbers, variables, or algebraic expressions.
1, 2, 6, and 12 are all divisors of 12 because they divide 12 equally. This is an important algebraic operation, which is used to simplify expressions, simplify fractions, and solve equations. This is also called algebraic factorization.
Factorization of x² + 2x - 3
x² + 3x - x - 3
(x² + 3x) - (x + 3)
x(x + 3) - 1(x + 3)
(x + 3)(x - 1)
Factorization of x² + 3x - 4
x² + 4x - x - 4
(x² + 4x) - (x + 4)
x(x + 4) - 1(x + 4)
(x + 4)(x - 1)
Factorization of x² - 2x - 3
x² - 3x + x - 3
(x² - 3x) + (x - 3)
x(x - 3) + 1(x - 3)
(x - 3)(x + 1)
Using identity, a² - b² = (a + b)(a - b)
x² - 9 = x² - 3²
x² - 3² = (x + 3)(x - 3)
Now, for the division:
(x² + 2x - 3)/(x² - 9) ÷ (x² + 3x - 4)/(x² - 2x - 3)
[(x + 3)(x - 1)/(x + 3)(x - 3)] ÷ [(x + 4)(x - 1)/(x - 3)(x + 1)]
By reciprocal of (x + 4)(x - 1)/(x - 3)(x + 1)
[(x + 3)(x - 1)/(x + 3)(x - 3)] × [(x - 3)(x + 1)/(x + 4)(x - 1)]
= (x + 1)/(x + 4)
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find the indefinite integral and check the result by differentiation. (use c for the constant of integration.) $$ \int \sqrt[3]{{\color{red}3} - {\color{red}4} x^2} ({\color{red}-8} x) \text{ }dx $$
The indefinite integral is - 1 / [5(6 + [tex]x^{5}[/tex])] + C.
An integral is considered to be indefinite if it has no upper or lower bounds. In mathematics, the most generic antiderivative of f(x) is known as an indefinite integral and expressed by the expression f(x) dx = F(x) + C. Without upper and lower bounds on the integrand, indefinite integrals are stated using the notation f(x), which represents the function as an antiderivative of F. Consequently, "f(x) dx=F" (x). As we observed in the same example with antiderivatives, the integral, x3 dx=14x4+C, is one example.
The area under the f(x) curve from x=a to x=b is represented by the definite integral of f(x), which is a NUMBER. Integral indefinite. An indefinite integral of a function f(x), also known as an antiderivative, is denoted by and its derivative is denoted by f. (x). The indefinite integral is not the only solution because the derivative of a constant is zero. Integration is the action of locating an indefinite integral.
Use a u-substitution with u = (6 + [tex]x^{5}[/tex])
du = 5[tex]x^{4}[/tex]dx
1/5 ∫ [tex]u^{-2}[/tex]du
= -1/5 [tex]u^{-1}[/tex] + C
= - 1 / [5(6 + [tex]x^{5}[/tex])] + C
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Correct Question:
Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.)
[tex]\int\limits^ {} \frac{x^{4} }{(6+x^{5})^{2} } dx[/tex]
Martha has a $200 deductible and 20% co-payment on her health
insurance. Last year she had $6,500 in medical bills. What was
Martha's out-of-pocket expense?
Answer:
Step-by-step explanation:
To solve this problem, we need to calculate Martha's out-of-pocket expenses, and the total amount of money she had to pay for her medical bills.
First, we need to calculate the amount of money Martha had to pay toward her deductible. Since her deductible is $200, this is the amount she had to pay out of pocket.
Next, we need to calculate the amount of money Martha had to pay toward her co-payment. Since her co-payment is 20%, we can calculate this by multiplying her medical bills by the co-payment rate: $6,500 x 0.2 = $1,300.
To find Martha's total out-of-pocket expense, we can add the amount she paid towards her deductible ($200) and the amount she paid towards her co-payment ($1,300):
$200 + $1,300 = $1,500
Therefore, Martha's out-of-pocket expense was $1,500.
Martha's insurance required her to pay a $200 deductible and a 20% co-payment on the remaining balance of her medical bills. After paying the deductible, she pays 20% of the remaining $6,300 which is $1,260. So, Martha's total out-of-pocket expense was $1,460.
Explanation:Martha's health insurance plan includes a $200 deductible and a 20% co-payment. The deductible is the amount Martha has to pay before the insurance company starts to pay. In this case, Martha first pays a $200 deductible from her $6,500 medical bills, which leaves her with $6,300 to be covered by insurance and her co-payment. The 20% co-payment means Martha is responsible for paying 20% of the remaining $6,300. To calculate this, we multiply $6,300 by 0.20 (20%), which equals $1,260. Therefore, Martha's total out-of-pocket expense for her medical bills last year was the $200 deductible plus the $1,260 co-payment, equalling $1,460.
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Leila works mowing lawns and babysitting.She earns $8.20 an hour for mowing and $7.90 and hour and babysitting.How much will she earn for 7 hours of mowing and 4 hours of babysitting?
Answer: 89
Step-by-step explanation:
1 hr of mowing = 8.20 dollars
1 hr of babysitting = 7.90 dollars
7 hrs of mowing = 8.20 x 7 = 57.4 dollars earned
4 hrs of babysitting = 7.90 x 4 = 31.6 dollars earned
Total amount she has earned = 57.4 + 31.6 + = 89 dollars
Please can someone explain this question to me step-by step, i have a exam this Wednesday so pleasee help me!! Help is greatly greatly appreciated ^^
Thankyou!!
Answer:
AB = 45.688 metres
Step-by-step explanation:
* i used a scientific calculator for my working. i am not sure if calculators are permitted for your exam on Wednesday *
⭐AB = AD + DB
⭐AB = 16.5 + DB
Thus, we need to find DB in order to solve for AB.
First, I utilized the triangle sum theorem to find ∠BDC:
[tex]< BDC + < DCB + < B = 180\\ < BDC + 59 + 90 = 180\\ < BDC + 149 = 180\\ < BDC = 31[/tex]
Then, I utilized the linear pair sum to find ∠ADC:
[tex]< ADC + < BDC = 180\\ < ADC + 31 = 180\\ < ADC = 149[/tex]
Next, I utilized the triangle sum theorem to find ∠DAC:
[tex]< DAC + < ADC + < ACD = 180[/tex]
[tex]< DAC + 149 + 10 = 180[/tex]
[tex]< DAC + 159 = 180[/tex]
[tex]< DAC = 21[/tex]
After, I utilized the law of sines to find DC:
[tex]\frac{sin10}{16.5} = \frac{sin21}{DC}[/tex]
[tex]DCsin10 = 16.5sin21[/tex]
[tex]DC = \frac{16.5sin21}{sin10}[/tex]
[tex]DC = 34.052[/tex]
Then, I utilized the sine function to find DB for ΔBDC:
[tex]sin(59) = \frac{DB}{34.052}[/tex]
[tex]34.052sin(59) = DB[/tex]
[tex]29.188 = DB[/tex]
Finally, I substituted DB into our original equation for AB:
[tex]AB = AD + DB[/tex]
[tex]AB = 16.5 + 29.188[/tex]
[tex]AB = 45.688 metres[/tex]
Good luck on your exam on Wednesday! :-)
The height of the pole will be equal to 45 meters.
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
Given that the angle BCD is 59 and the angle BCA is 69. The height will be calculated as,
tan(59) = BD / BC
BC = BD / tan(59)
BC = 0.6BD
tan(69) = AB / BC
tan(69) = ( 16.5 + BD ) / BC
BC = 0.38( 16.5 + BD )
Equate the values of BC,
0.6BD = 0.38 ( 16.5 + BD )
0.6BD = 6.27 + 0.38BD
0.22BD =6.27
BD = 28.5 meters
The height of the pole is,
AB = AD + DB
AB = 16.5 + 28.5
AB = 45 meters
The height is 45 meters.
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Steven found that between 2012 and 2020, as a country's per capita chicken egg consumption increased, the country's divorce rate decreased. Based on this information, which of the following conclusions is valid?
O Eating chicken eggs prevents divorces.
O Divorces lead to a decrease in per capita chicken egg consumption.
O There is a positive association between per capita chicken egg consumption and divorce rate.
O There is a negative association between per capita chicken egg consumption '.' and divorce rate
There is a positive association between per capita chicken egg consumption and divorce rate is true.
Define statement.A statement in mathematics is a declarative utterance that can only be either true or false. A proposal is another name for a statement. It's important that there be no ambiguity. A sentence can only be true or untrue and not both for it to be a statement.
Give example of statement.A meaningful string of words that can be either true or incorrect makes up a mathematical statement. They are referred to simply as a statement. For instance, "ABC is an equilateral triangle" could be denoted by the letter "p." As a result, in an equilateral triangle, p = ABC.
There is a positive association between per capita chicken egg consumption and divorce rate is the correct and valid statement according to the given presented situation.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
The minimal set of coordinates required to represent any point inside a mathematical space is known as the dimension of the space in physics and mathematics.
What is 3D and 2D ?The terms 2D and 3D describe the precise sizes of a computer workstation. Using the horizontal and vertical (X and Y) axes, 2D is "flat," meaning that there are only two dimensions to the picture, which becomes a line when rotated to the side. The depth (Z) dimension is added in 3D.A two-dimensional form known as a "2D shape" is characterised by its horizontal and vertical axes (x-axis and y-axis)The three spatial dimensions of width, height, and depth are referred to as three dimensions, or 3D. The physical world is three dimensional, as is everything that can be seen there.The rectangle, square, circle, triangle, and any other polygon are a few examples of 2D forms. Cuboid, cube, sphere, cone, prism, cylinder, pyramid, etc. are a few examples of 3D forms.Fill in blanks :
A point has no dimension. it is an abstract idea of a location in space.
A vertex is where two edges meet at a point
A line has edge dimension - length . An edge is a line segment where two faces meet.
A flat plane figures has a 2 dimension - length and width
The 3 points of a 3D object is a plane.
Three dimensional objects have vertices, edges and faces unless they are the geometric solids like cylinders, cones and sphere.
when we talk about line we are looking at the measure of a one dimensional figure.
when we talk about area we are looking at the space inside of a two dimensional figure.
when we talk about volume we are looking at the total space enclosed by a three dimensional figure.
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Solve the following inequality.4x+6<3x+3
Answer:
x < - 3
Step-by-step explanation:
4x + 6 < 3x + 3 ( subtract 3x from both sides )
x + 6 < 3 ( subtract 6 from both sides )
x < - 3
Answer:
x < -3
Step-by-step explanation:
4x+6<3x+3
= 4x+6-3x<3
= 4x-3x<3-6
4x-3x<3-6
=x<3-6
x<-3
given the function h(x)=8x-3/4x+5 as the values of x increase towards infinity, use a table to find out what happens to the values of h(x)
according to question,
given data.
h(x)=8x-3/4+5
then,
could any one please help me with this question
Answer:
10°
Step-by-step explanation:
The sum of the measures of the exterior angles of any polygon, one per vertex, is 360°.
x + 3x + 4x + 5x + 6x + 8x + 9x = 360
36x = 360
x = 10
In a polygon, an exterior angle is supplementary to its adjacent interior angle.
The smallest exterior angle is x, and x = 10.
Answer: 10°
What is the equation in slope-intercept form of the line that crosses the x-axis at 14 and is parallel to the line represented by y= -2/3x+6
The equation in slope intercept for the given line is y = -2/3x - 28/3.
What is Slope ?
The slope or gradient of a line in mathematics is a number that indicates the line's steepness and direction.
Given, the line crosses the x-axis at 14 and is parallel to the line represented by y= -2/3x+6.
We know that two parallel lines always have the same slope.
We can say that the line has coordinate as (14,0) and slope (m) as -2/3.
We know that the slope-intercept form of the line is,
y= mx + b
Now, We put x=14, y=0 and m=-2/3 in equation above,
We get, 0 = -2/3 × 14 + b
b = -28/3
So, the slope intercept form will be :
y = -2/3x - 28/3
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One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant. The responses for a sample of n = 10 students are summarized in the frequency distribution. What is the best measure of central tendency for these data?
X f
5+ 2
4 3
3 2
2 1
1 1
0 1
Answer:
the mean (i.e. the average)
Step-by-step explanation:
There's no clear outlier or inconsistency therefore the mean should be used.
Pleas Help ASAP Giving brainliest if correct <3
Answer: the first one is 7/9 and the second one is option 2
Step-by-step explanation:
4+7 = 11
< or> = open dot
which of the following conditions must be met to conduct a two-proportion significance test? the populations are independent. the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population. each sample is a simple random sample.
All the given three conditions are true for conducting a two proportion significance test.
To check the significance of two proportions, following conditions should be met
Data of each group must be collected from the population using a random sampling. That means data values must be independent.Population should be independent of each other.The two populations must be approximately or normally distributed. To check the assumption of the normality, we have the following condition: “The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.” If this condition is met, we say that populations are normally distributed.Hence, all the three conditions must be met to conduct a two-proportion significance test.
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Which rational expression is equivalent to this expression?
4/x-3. A) X-3/x+2•x+2/4. B) X-3/x+2/ 4/x+2. C) x+2/x-3• 4/x+2. D) x+2/x-3/ 4/x+2
The rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.
What is rational function?A rational function is one that can be written as a polynomial divided by a polynomial. The domain of a rational function is the set of all numbers except the zeros of the denominator.Given is the expression as follows -
f(x) = 4/(x - 3)
[A] -
{x - 3/x + 2} • {x + 2/4} = {x - 3/4}
[B] -
{x - 3}/{x + 2} / {4/x + 2} = {x - 3}/{x + 2} × {x + 2/4} = {x - 3/4}
[C] -
{x + 2/x - 3} • {4/x + 2} = {4/x - 3}
[D] -
{x + 2/x - 3} / {4/x + 2} = {(x + 2)²/ 4x - 3}
Therefore, the rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.
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May someone help me with this?
Step-by-step explanation:
0 hours -> $500 total cost
1 hour -> $575 total cost (500 + 1×75)
2 hours -> $650 total cost (500 + 2×75)
3 hours -> $725 total cost (500 + 3×75)
P(t) = 75t + 500
A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. The mean braking distance for SUVs equipped with tires made with compound 1 is 41 feet, with a population standard deviation of 12.1. The mean braking distance for SUVs equipped with tires made with compound 2 is 46 feet, with a population standard deviation of 9.0. Suppose that a sample of 66 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ1 be the true mean braking distance corresponding to compound 1 and μ2 be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance.
State the null and alternative hypotheses.
Determine critical value.
Calculate value of test statistic. Round your answer to two decimal places.
State conclusions
The critical value is -2.70
What is a null hypothesis?
Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance. It is feasible to estimate the probability that the null hypothesis is correct using statistical testing.
Here, we have
The objective of this experiment is to compare two compounds, designed to reduce braking distance, used in tire manufacturing to prove if the braking distance of SUVs equipped with tires made with compound 1 is shorter than the braking distance of SUVs equipped with tires made with compound 2.
So you have 2 independent populations, SUV's equipped with tires made using compound 1 and SUVs equipped with tires made using compound 2.
Two samples of 66 braking tests are made and the braking distance was measured each time, the study variables are determined as:
X₁: Braking distance of an SUV equipped with tires made with compound one.
Its sample mean is X[bar]₁= 41 feet
And the Standard deviation S₁= 12.1 feet
X₂: Braking distance of an SUV equipped with tires made with compound two.
Its sample mean is X[bar]₂= 46 feet
And the Standard deviation S₂= 9.0 feet
We don't have any information on the distribution of the study variables, nor the sample data to test it, but since both sample sizes are large enough n₁ and n₂ ≥ 30 we can apply the central limit theorem and approximate the distribution of both variables sample means to normal.
The researcher's hypothesis, as mentioned before, is that the braking distance using compound one is less than the distance obtained using compound 2, symbolically: μ₁ < μ₂
The statistical hypotheses are:
H₀: μ₁ ≥ μ₂
H₁: μ₁ < μ₂
α: 0.05
The statistic to use to compare these two populations is a pooled Z test
Z= {(X[bar]₁-X[bar]₂) - (μ₁ - μ₂)}/√S₁²/n₁+S₂²/n₂ ≈ N(0;1)
Z = {(41-46)-0}/√146.41/66+81/66
Z = -5/1.85
Z = -2.70
The rejection region of this hypothesis test is one-tailed to the right, so you'll reject the null hypothesis to small values of the statistic. The critical value for this test is:
Z(α) = Z(0.05) = -1.645
Decision rule:
If Z(H₀) ≥ -1.645, then you do not reject the null hypothesis.
If Z(H₀) < -1.645, then you reject the null hypothesis.
Since the statistic value is greater than the critical value, the decision is to not reject the null hypothesis.
At a 5% significance level, you can conclude that the average braking distance of SUVs equipped with tires manufactured used compound 1 is greater than the average braking distance of SUVs equipped with tires manufactured used compound 2.
Hence, the critical value is -2.70.
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Solve. p/1 6/7=−4.4(refer to the picture)
enter your answer as a mixed number in simplest form in the box.
Answer:
p = -8 6/35
Step-by-step explanation:
p/(1 6/7)=−4.4
To solve for p, multiply each side by 1 6/7
p/(1 6/7) * ( 1 6/7)=−4.4 * (1 6/7)
p = - 4.4 * ( 1 6/7)
Change each number to fractions
p = -44/10 * 13/7
p = -286/35
Change to a mixed number
p = -8 6/35
NO LINKS!!
A total of $28000 is invested in 2 municipal bonds that pay 5.75% and 7.25% simple interest. The investor wants an annual interest income of $1790 from the investments. What amount should be invested in the 5.75% bond?
Answer:
$16,000
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
I = Interest accruedP = Principal amountr = Interest rate (in decimal form)t = Time (in years)Let investment 1 be the bond that pays 5.75% simple interest.
Let investment 2 be the bond that pays 7.25% simple interest.
Given:
P₁ + P₂ = $28,000r₁ = 5.75% = 0.0575r₂ = 7.25% = 0.0725t = 1 yearCreate two equations for the interest from both investments.
Interest from Investment 1
[tex]\implies \sf I_1=P_1 \cdot 0.0575 \cdot 1[/tex]
[tex]\implies \sf I_1=0.0575\:P_1[/tex]
Interest from Investment 2
[tex]\implies \sf I_2=P_2 \cdot 0.0725 \cdot 1[/tex]
[tex]\implies \sf I_2=(28000-P_1)0.0725[/tex]
[tex]\implies \sf I_2=2030-0.0725\:P_1[/tex]
Given that the sum of the interest from both investments is $1,790:
[tex]\implies \sf I_1+I_2=1790[/tex]
[tex]\implies \sf 0.0575\:P_1+2030-0.0725\:P_1=1790[/tex]
[tex]\implies \sf -0.015\:P_1=-240[/tex]
[tex]\implies \sf P_1=16000[/tex]
Therefore, $16,000 should be invested in the 5.75% bond.
Check:
[tex]\implies \sf I_1=16000 \cdot 0.0575 \cdot 1 = 920[/tex]
[tex]\implies \sf I_2=12000 \cdot 0.0725 \cdot 1 = 870[/tex]
[tex]\implies \sf I_1+I_2=920+870=1790[/tex]
2. Calculate On landing, the plane touches the runway with a speed of 65 m/s. The figure shows the speed of the plane after 1 second. Calculate the acceleration of the plane during its landing.
The plane touches the runway with a speed of 65 m/s then the acceleration of the plane during its landing will be equal to 65 m/s².
What is acceleration?The rate of change in an object's velocity concerning time is known as acceleration in mechanics. The vector quantity of accelerations. The direction of the net force that is acting on an object determines its acceleration.
Since acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is a vector quantity as well. The definition of acceleration is the change in velocity vector over a time interval divided by the time interval.
As per the given information in the question,
Velocity, v = 65 m/s
Time, t = 1 sec.
Use the equation of acceleration,
a = v/t
a = 65/1
a = 65 m/s²
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What is 37,056 rounded to the nearest thousand?
Answer:
Step-by-step explanation:
40k
A store charges a rate per minute plus a flat fee to rent cleaning supplies. A 30 minute rental $110.50. A 40 minute rental costs $145. How much for a 25 minute rental
The cost of a 25-minute rental will be $92.00.
To find the amount a 25-minute rental would cost, we need to first determine the rate per minute and the flat fee. We can do this by setting up the following system of equations:
30 minutes x rate + flat fee = $110.50
40 minutes x rate + flat fee = $145
To solve this system of equations, we can multiply the first equation by 2 and subtract the second equation from it to eliminate the rate:
(30 minutes x 2) x rate + flat fee x 2 = 2 x $110.50
80 minutes x rate + flat fee x 2 = 2 x $110.50
Subtracting the second equation from the first equation, we get:
flat fee x 2 - flat fee x 2 = 2 x $110.50 - 2 x $145
flat fee x 2 - flat fee x 2 = -$34.50
Since the left side of the equation is equal to zero, we can divide both sides by 2 to solve for the flat fee:
flat fee - flat fee = -$34.50 / 2
flat fee - flat fee = -$17.25
Since the left side of the equation is also equal to zero, the flat fee must be zero.
We can now use either of the original equations to solve for the rate per minute. Using the first equation, we get:
30 minutes x rate + flat fee = $110.50
30 minutes x rate = $110.50
rate = $3.68
We can now use this rate to find the cost of a 25-minute rental:
25 minutes x $3.68 + flat fee = $92.00 (Since the flat fee is zero)
Thus, a rental of 25 minutes costs $92.00.
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Two logarithmic functions are graphed f(x) = log (x) and g(x) = log3(x). Describe the effect on the shape of their graphs.
Responses
ABy decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.
By decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.
BBy decreasing the base number the graph was affected horizontally. A lower base number caused the graph to spread out faster along the x-axis.
By decreasing the base number the graph was affected horizontally. A lower base number caused the graph to spread out faster along the x-axis.
CBy decreasing the base number the graph was affected horizontally. A lower base number caused the graph to become more compressed.
By decreasing the base number the graph was affected horizontally. A lower base number caused the graph to become more compressed.
DBy decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a faster rate.
A. By decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.
What is a logarithm function?
The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 10³, its logarithm in base 10 is 3, or log₁₀ 10³= 3.
Given function are
f(x) = log x and g(x) = log₃ x.
The rate of raise of the graph g(x) is more than that of the graph f(x).
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Please Help! I need this by tomorrow! I will give BRAINLIEST
The number of bacteria in a sample is increasing according to an exponential model. After four hours, the sample contained 400 bacteria. After twelve hours, the sample contained 1,600 bacteria. Write an exponential growth model for the number of bacteria in the sample after x hours.
The solution is Option A.
The exponential growth model for the number of bacteria in the sample after x hours is [tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]
What is exponential growth factor?
The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the equation for the number of bacteria in the sample after x hours = P
The value of the equation P ( x ) is given by
After 4 hours , the sample contained 400 bacteria
So ,
when x = 4
[tex]P ( 4 ) = ae ^{4b }=400[/tex] be equation (1)
After 12 hours , the sample contained 1600 bacteria
And , when x = 12
[tex]P ( 12 ) = ae ^{12b }=1600[/tex] be equation (2)
Divide equation (2) by equation (1) , we get
[tex]\frac{P ( 12 )}{P ( 4 )} = \frac{ae ^{12b }}{ae ^{4b }} = \frac{1600}{400}[/tex]
On simplifying the equation , we get
e¹²ᵇ⁻⁴ᵇ = 4
e⁸ᵇ = 4
Taking logarithm on both sides of the equation , we get
8b = ln (4)
Divide by 8 on both sides , we get
b = ln (4) / 8
Substituting the value for b in equation (1) , we get
[tex]ae ^{4*ln (4) / 8 }=400[/tex]
[tex]ae ^{ln (4) / 2}=400[/tex]
On simplifying the equation , we get
a x 2 = 400
Divide by 2 on both sides of the equation , we get
a = 200
Therefore , the exponential growth equation is given by
Substitute the values of a and b in the equation , we get
[tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]
Hence , The exponential growth model for the number of bacteria in the sample after x hours is [tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]
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30-(-2)*(-10)+(-5)-(-2)=
Answer:
Step-by-step explanation:
-2 * -10 = 20
Answer:
30×2×(-10)-5+2
=60×(-10)-3
=-60-3
=-63
Assume that a random variable is normally distributed with a mean of 1,300 and a variance of 271. Complete parts a
through c below.
a. What is the probability that a randomly selected value will be greater than 1,350?
The probability is
(Round to four decimal places as needed.)
Answer:
I believe if I just believe that you can work this out then you can do it thank you You are intelligent you can do this
calculating Nominal GDP, Real GDP, and other economic indicators and can successfully use these indicators to draw conclusions because…
You can successfully use nominal GDP, real GDP, and other economic indicators to draw conclusions because they health of the country's economy.
What is GDP?GDP stands for Gross Domestic Product. This is a very common economic indicator that shows the value of the services and products produced by a country usually in a one year period.
What is the difference between real and nominal GDP?In general real GDP is considered to be more accurate as nominal GDP is influenced by factors such as inflation that can distort the general idea you can get about a country's economy and the total output of it.
What do economic indicators reveal?Both real, nominal GDP and other indicators show the health of the economy in a country, which makes it useful to draw conclusions about the economy.
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