ANSWER
A. x ≥ -5 and x < 4
EXPLANATION
We have the two inequalities:
- 4x + 1 ≤ 21 and 5x + 2 < 22
Let us solve them separately:
FIRST ONE
-4x + 1 ≤ 21
Collect like terms:
-4x ≤ 21 - 1
-4x ≤ 20
Divide through by -4, the sign changes:
[tex]\begin{gathered} x\ge\text{ }\frac{20}{-4} \\ x\text{ }\ge\text{ -5} \end{gathered}[/tex]SECOND ONE
5x + 2 < 22
Collect like terms:
5x < 22 - 2
5x < 20
Divide through by 5:
x < 20 / 5
x < 4
The answer is Option A.
Solve the equation for y in terms of x. In other words, algebraicallyrearrange the equation so that the y variable is by itself one side of theequation. Type your answer in the form y = mx + b. If you have a valuethat is not an integer then type it rounded to the nearest hundredth. Donot put spaces between your characters.4.2 + 2y = 8y = ?4x+2y=8
Given:
[tex]4x+2y=8[/tex]Solve the equation for y,
[tex]\begin{gathered} 4x+2y=8 \\ Subtract\text{ -4 from both sides} \\ 4x+2y-4x=8-4x \\ 2y=8-4x \\ \text{Divide by 2 on both side} \\ \frac{2y}{2}=\frac{8-4x}{2} \\ y=\frac{8}{2}-\frac{4x}{2} \\ y=4-2x \\ \text{ express the equation in the form y=mx+b} \\ y=-2x+4 \end{gathered}[/tex]Answer: y = -2x +4
Find the suma1 = -26/5 , d = -5/3 , n = 10
The sum of the arithmentic series is -127
Step - by - Step Explanation
What to find? The sum of the arithmetic series.
Parameter Given:
a₁ = -26/5 , d=-5/3 , n=10
To find the sum of the arithmetic series we will use the formula below:
[tex]S=\frac{n}{2}\mleft\lbrace2a+(n-1)d\mright\rbrace[/tex]Substitute the values and evaluate.
[tex]S=\frac{10}{2}\mleft\lbrace2(\frac{-26}{5}_{})+(10-1)(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace2(\frac{-26}{5})+9(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace-\frac{52}{5}-15\mright\rbrace[/tex][tex]=-52-75[/tex]=-127
what is 4 divided by 1 over2
Answer:
4/1÷2 =4×1/2
Step-by-step explanation:
You have to invert and then multiply
so the answer will be 2
Estimate [tex] \sqrt[3]{20} [/tex] between two integers.
Answer
∛20 is between 2 and 3.
Explanation
The question asks us to find the cube root of 20.
∛20
The key to doing this without the calculator is to take the cube of numbers and the one that has 20 in between them is the answer.
1³ = 1
2³ = 8
3³ = 27
We can see that 20 is between 8 and 27.
So,the cube root of 20 has to be betwen 2 and 3.
The other way to do this with the calculator is to actually find the cube root of 20
∛20 = 2.71
Which is between 2 and 3.
Hope this Helps!!!
5. Evaluate the following V16
The directress of a parabola is represented by the linear equation y=2, and its vertex is located at (3,1).Both of these attributes of the parabola are graphed below. which of the following is the equation that represents this parabola?
The directrix of the parabola is at y = 2 and its vertex is at (-3,1). Since the directrix is below the vertex, we can say that the parabola will open downwards. The general form to find the equation of the parabola given the directrix and vertex is
[tex]y=-(x-h)^2+k[/tex]The value of h for the problem is -3 while the value of k for the problem is 1. Substitute it on the equation above, we get
[tex]\begin{gathered} y=-(x-(-3))^2+1 \\ y=-(x+3)^2+1 \end{gathered}[/tex]Hence, the answer to this problem is option 2. Note that the equation started in a negative sign because the parabola opens downwards.
40 POINTSSSSS!!!!!!!!!! PLS HELP NO LOOKING IT UP!A polygon is shown on the graph: What effect will a translation 3 units down and 2 units left have on the polygon? Be sure to address how it could impact the angles, side lengths, and congruency between the original pre-image and the image.
we know that
A translation is a rigid transformation
In a translation the preimage and the image are congruent
that means -----> the angles and side lengths of the image and the preimage are congruent (are equal)
The only difference between the image and the preimage is the location
Remember that
If two figures are congruent, then their corresponding angles and their corresponding sides are equal
1/2(4×5)-2³= what's the awnser
Explanation:
[tex]\frac{1}{2}(4\times5)-2^3=[/tex]First we have to solve the products, divisions and powers in each term. The terms are separated by + or - signs. In this expression there are two terms.
In the first term there's a product inside a parenthesis. This means that we have to solve that first:
[tex]=\frac{1}{2}\cdot20-2^3[/tex]Now we can solve the multiplication in the first term:
[tex]=10-2^3[/tex]Solve the power in the second term:
[tex]=10-8[/tex]And do the substraction:
[tex]=2[/tex]Answer:
1/2(4x5) - 2³ = 2
State the null and alternative hypotheses for the claimA report from five years ago said that the average income of accountants was $51,497; but nowadays it's more than that.
ANSWER and EXPLANATION
We want to state the null and alternative hypotheses for the claim given.
A null hypothesis is a statement about a population parameter such that the likelihood can be tested to either accept or reject the alternative hypothesis.
An alternative hypothesis on the other hand is a statement that directly contradicts the null hypothesis.
Therefore, going by that, we see that the null hypothesis is:
[tex]\mu=\$51,497[/tex]and the alternative hypothesis is:
[tex]\mu>\$51,497[/tex]Can somebody Answer this?
Garry needs 18.4 oz of glue and 9.2 oz of glitter to make 4 bottles.
What is direct proportion?In direct proportion between two or more than two quantities if one quantity is multiplied or divided by some constant k other quantities will also be multiplied or divided by the same constant k.
Given, Making 1 bottle of glitter glue Garyy requires 4.6 oz of glue and 2.3 oz of glitter.
∴ 4 bottles of glitter glue require (4.6×4) = 18.4 oz of glue and (2.3×4) = 9.2 oz of glitter.
As the no. of bottles is multiplied by 4 thus material requirements will also be multiplied by a factor of 4.
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Please show and explain this please
The graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.
What is a graph of a function?Defining a function's graph: The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We could also say that the graph of f is the graph of y = f(x). As a result, the graph of an equation is a particular instance of the graph of a function. We merely select a value for x, then determine the value of y that corresponds. Equations that have been solved for y are graphed as functions! In this instance, the graph of f(x) is the graph of y = x² - 3. Making points for the graph is simple.So, the function with which the given graph matches:
The graph of the option (E) f(x) = (x + 10)(x - 3)²(x + 1) is:(Refer to the graph attached below)We can easily see that coordinates of the given graph and the graph of equation (E) match.Therefore, the graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.
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ach function is a transformation of the parent sine function. Based on the period, which graph represents each transformed function?
Given the functions:
• f(x) = sin(-x)
,• f(x) = sin(2x)
,• f(x) = sin(1/2x)
Given that each function is a transformation of the parent sine function, let's select the graph which represents each transformed function.
We have the parent sine function:
f(x) = sin(x).
• For function A.
f(x) = sin(-x)
The graph of this transformed function will be:
• For function B.
f(x) = sin(2x)
The period of this function will be:
[tex]T=\frac{2\pi}{B}=\frac{2\pi}{2}=\pi[/tex]Therefore, the graph which represents this function is:
• Function C.
f(x) = sin(1/2x)
The period of this function will be:
[tex]T=\frac{2\pi}{B}=\frac{2\pi}{\frac{1}{2}}=4\pi[/tex]Therefore, the graph of this function will be:
ANSWER:
6. The National Institute of Health is studying the relationship between number of
smoked per day and the birth weight of babies born to mothers who
smoke cigarettes. A sample of the 6 points is selected are listed below.
cigarettes
No. of Cigarettes per day (X) 22 13 29 11 28 6
Birth weight (Y)
6.1 7.9 5.8 7.4 6.3 8.2
Compute Pearson's sample correlation coefficient.
Compute the equation of the least squares regression line.
ŷ
=
What is the predicted baby weight born for a mother smoke 40 cigarettes per day.
Using the calculator for the line of best-fit, the measures are given as follows:
Correlation Coefficient: -0.9405.Regression Line: y = -0.1x + 8.77.Baby weight for the mother that smokes 40 cigarettes a day: 4.77 grams.How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) given in the problem in the calculator. These points are given on a table or in a scatter plot in the problem.
From the given table, the points in this problem are as follows:
(22, 6.1), (13, 7.9), (29, 5.8), (11, 7.4), (28, 6.3), (6, 8.2).
Hence:
The correlation coefficient is of -0.9405.The regression line is of: y = -0.1x + 8.77.Hence, for a mother that smokes 40 cigarettes on a day, the predicted weight is of:
y = -0.1(40) + 8.77 = 4.77 grams.
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find the distance from line y= -3x + 4 to line y = -3x - 1
A tank has two inlet pipes and one outlet pipe. The inlet pipes can fill the tank in 4 hoursand 10 hours. The outlet pipe can drain the tank in 2 hours. One day the outlet pipe was leftopen as the empty tank was being filled. Will the tank ever be full? If so, how long will ittake to fill the tank? If not, explain why not.
The two inlet pipes can fill the tank in 4 hours and 10 hours.
The work done by the inlet pipes per hour is calculated to be:
[tex]\Rightarrow\frac{1}{4}+\frac{1}{10}=\frac{7}{20}\text{ units per hour}[/tex]The outlet pipe drains the tank in 2 hours. The work done will be:
[tex]\Rightarrow\frac{1}{2}\text{ units per hour}[/tex]Therefore, if both inlet pipes and the outlet pipes are opened at the same time, the work done by the pipes combined will be:
[tex]\Rightarrow\frac{7}{20}-\frac{1}{2}=-\frac{3}{20}\text{ units per hour}[/tex]Since the work done to fill the tank is negative, it means that the tank will never get full as it empties faster than it fills up.
find the 12th term of the series; 0.008, 0.04, 0.2
Answer
12th term = 390,625
Explanation
On close observation, we can see that the given series is in geometric progression.
Geometric progression has a general formula of
aₙ = a (rⁿ⁻¹)
where
aₙ = nth term
a = First term
r = Common ratio
n = number or position of the term
For this question, we need to compute the common ratio
Common Ratio = (Next term) ÷ (Current term)
= (Second term) ÷ (First term)
= (Third term) ÷ (Second term)
For this question,
Common Ratio = 0.04 ÷ 0.008 = 5
OR
0.2 ÷ 0.04 = 5
And we can see that the first term is 0.008
So, the 12th term will have the formula
aₙ = a (rⁿ⁻¹)
a = 0.008
n = 12
r = 5
a₁₂ = 0.008 (5¹²⁻¹)
= 0.008 (5¹¹)
= 0.008 (48,828,125)
= 390,625
Hope this Helps!!!
K
A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the mean salary.
Salary ($) Employees
5,001-10,000
10,001-15,000
17
15
15,001-20,000
20,001-25,000
25,001-30,000
OA. $7,376.62
B. $17,625
C. $15,862.50
D. $19,387.50
16
13
19
The mean salary of the employees is $17625.5.
The total number of employees in the company is 80.
The total salary for the first interval is [(5001+10000)/2]*17 = 127508.5.
The total salary for the second interval is [(10001+15000)/2]*15 = 187507.5.
The total salary for the third interval is [(15001+20000)/2]*16 = 280008.
The total salary for the fourth interval is [(20001+25000)/2]*13 = 292506.5.
The total salary for the fifth interval is [(25001+30000)/2]*19 = 522509.5.
In math, a mean is the average of a data collection, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers. The mean salary is the sum of all salaries divided by the total number of employees.
M = (127508.5 + 187507.5 + 280008 + 292506.5 + 522509.5)/80
M = 17625.5
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Write an explicit equation for the arithmetic sequence defined byt(n+1)= t(n)-4t(2) = 10
We need to find the explicit equation for the sequence:
[tex]\begin{gathered} t\mleft(n+1\mright)=t\mleft(n\mright)-4 \\ \\ t(2)=10 \end{gathered}[/tex]First, we can complete the given table. Notice that when we subtract 4 from the n-th term, we obtain the next term (n+1).
Then, to find a previous term, we can add 4. Thus. we obtain:
n t(n)
0 14+4 = 18
1 10+4 = 14
2 10
3 10-4 = 6
4 6-4 = 2
5 2-4 = -2
Now, observing the above relations, we need to write an expression for t(n) in terms of n:
n t(n)
0 18 = 18 - 0*4
1 14 = 18 - 1*4
2 10 = 18 - 2*4
3 6 = 18 - 3*4
4 2 = 18 - 4*4
5 -2 = 18 - 5*4
...
n 18 - n*4
Therefore, an explicit equation for the sequence is:
[tex]t(n)=18-4n[/tex](1/5) -1 as the exponent
Answer:
1/5
Step-by-step explanation:
what is the ratio of 12
Answer:
12.:1 Is the great answer of this question
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: 0, ordered pair: (−3,−8)
The equation (in slope-intercept form) of the line as described whose slope is; 0 and passes through the point given is; y = -8.
What is the equation of the line whose slope is; 0 and passes through the point given;It follows from the task content that the equation of the line whose slope is; 0 and passes through the point; (-3, -8) is to be determined.
Hence, from the slope formula;
slope, m = ∆y/∆x
Therefore; 0 = ∆y/∆x
By cross-multiplication; we have;
∆y = 0
Recall, ∆y = y - y1 = y - (-8)
y - (-8) = 0
y + 8 = 0
y = -8.
Therefore, it follows that the equation of the line described is; y = -8.
Consequently, the line in discuss is a horizontal line.
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The length of a rectangle is six times its width.
If the perimeter of the rectangle is 84 m, find its area.
The area when the length of a rectangle is six times its width is 216m².
How to calculate the value?Let the width = w
Let the length = 6 × w = 6w
Therefore the perimeter will be:
= 2(Length + Width) = 84
2(w + 6w) = 84
2 × 7w = 84
14w = 84
Divide
w = 84 / 14
w = 6
Width = 6m
Length = 6w = 6 × 6 = 36m
The area will be:
= Length × Width
= 36m × 6m
= 216m²
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Alan mose lawn in the summer to make money he knows that on an average he can mow 1/2 of a lawn in 1/4 hours calculate his average mowing rate in lawns per hour
Answer:
2 Lawns Mowed per hour
Step-by-step explanation:
This question requires the concept of: Conversion.
ConversionThe concept of Conversion is about converting to a certain unit value.
Example: 24 Sour Plums per 2 baskets = 12 Sour Plums per basket.
Application:For this question, we are asked to convert the unit from 0.25 hours to 1 hour.
(Note: 1/4 hours = 0.25 hours)
0.25 hours = 0.5 Lawn Mowed
(0.25 ÷ 0.25) hours = (0.5 ÷ 0.25) Lawn Mowed
1 hour = 2 Lawns Mowed per hour.
Note: You can use fractions to solve the problem, it will give you the same result.
a Fill in the blank. If necessary, use the slash mark (/) for a fraction bar. If cosg = then tang =
We can use a right triangle and the below trigonometric ratios.
[tex]\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent leg}}{\text{ Hypotenuse}} \\ \tan(\theta)=\frac{\text{ Opposite leg}}{\text{ Adjacent leg}} \end{gathered}[/tex]In this case, we have:
[tex]\cos(\theta)=\frac{3}{5}=\frac{\text{Adjacent leg}}{\text{Hypotenuse}}[/tex]As we can see, we need to know the value of the opposite leg. Since it is a right triangle, we can use the Pythagorean theorem formula.
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where} \\ a\text{ and }b\text{ are the legs} \\ c\text{ is the hypotenuse} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a=3 \\ b=? \\ c=5 \\ a^{2}+b^{2}=c^{2} \\ 3^2+b^2=5^2 \\ 9+b^2=25 \\ \text{ Subtract 9 from both sides} \\ 9+b^2-9=25-9 \\ b^2=16 \\ $$\text{ Apply square root to both sides of the equation}$$ \\ \sqrt{b^2}=\sqrt{16} \\ b=4 \end{gathered}[/tex]Finally, we have:
Then, we can find the value of tan(θ):
[tex]\begin{gathered} \tan(\theta)=\frac{\text{Opposite leg}}{\text{Adjacentleg}} \\ \tan(\theta)=\frac{4}{3} \end{gathered}[/tex]Answer[tex]\tan(\theta)=\frac{4}{3}[/tex]Someone please help me with this!
The width of the chest is 14.7 inches.
What is a Rectangular Prism?A rectangular prism is a three-dimensional form with six faces, where all of the faces (top, bottom, and lateral faces) are rectangles and all pairings of opposite faces are congruent. The volume of a rectangular prism is the space that it contains. We know that the volume of any prism is calculated by multiplying its base area by its height.Given:
The volume of rectangular prism = 10368 cubic inches or 6 cubic feet
Height of rectangular prism = 24 inches
It is mentioned that the chest will be twice as long as it is wide.
Let the width of the chest be x inches, so its length is 2x inches.
The volume of the chest = length × width × height
Substituting the values,
10368 = 2x × x × 24
10368 = 2x²× 24
x² = 10368/48
x = √216
x ≅ 14.7 inches ( to the nearest tenth of an inch)
Therefore, the width of the chest is 14.7 inches.
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A skating rink charges a group rate of $9 plus a fee to rent each pair of skates. A family rents 7 pairs of skates and pays a total of $30.
Answer: One pair of skates costs a total of $3
Step-by-step explanation: 30 (Total) - 9 (Fee) ÷ 7 (Pairs of skates)
Total - Free ÷ Pair of skates
Find the total surface area of the cone. Use the r button on your calculator. altitude = 13 cm, diameter = 11 cm, slant height = 15 cm
In general, the area of a cone is given by the formula below
[tex]\begin{gathered} A=\pi r^2+\pi rl \\ r\rightarrow\text{ radius} \\ l\rightarrow\text{ slant height} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} r=\frac{11}{2}=5.5 \\ l=15 \\ \Rightarrow A=\pi *5.5^2+\pi *5.5*15 \\ \Rightarrow A=112.75\pi \end{gathered}[/tex]Rounding to two decimal places,
[tex]\Rightarrow A\approx354.22[/tex]The answer is approximately 354.22 cm^, option D.A school is organising a fun runThe fun run involves a 5
1
2
mile run around the field, then a 5
4
7
mile run back to the school. Find the total distance of the fun run.Give your answer as a mixed number in its simplest form.
In mixed fraction the total distance of the fun run is 11 1/14
A school is organising a fun run. The fun run involves a 5 1/2
mile run around the field, then a 5 4/7 mile run back to the school.
The total distance is equal to summation of run around the field and run back to school.
total distance = 5 1/2 + 5 4/7
= 11/2 + 39/7
The L. C. M of 2 and 7 is 14
= [tex]\frac{11.7}{2.7} + \frac{39.2}{7.2}[/tex]
(77 + 78)/14
155/14
Upon dividing 155 by 14, the quotient is 11 and the the remainder is 1
In mixed fraction it is 11 1/14
So in mixed fraction the total distance of the fun run is 11 1/14
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Length is 3x − 4, area is 6x4 − 8x3 + 9x2 − 3x − 12
The width of the given rectangle is 2x²-3x+3.
Given that, area of rectangle = [tex]6x^4-8x^3+9x^2-3x-12[/tex] and the length of rectangle = 3x-4.
What is the area of a rectangle?The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units. The formula to find the area of a rectangle = Length × Width.
Now, (3x-4) × width = [tex]6x^4-8x^3+9x^2-3x-12[/tex]
⇒ Width = [tex]\frac{6x^4-8x^3+9x^2-3x-12}{3x-4}[/tex]
3x-4|[tex]6x^4-8x^3+9x^2-3x-12[/tex]|2x³-3x+3
[tex]6x^4[/tex] - 8x³
_________________
0+9x²-3x-12
(-) 9x²+12x
_________________
0+9x-12
(-) 9x(+)12
_________________
0
So, width = 2x²-3x+3
Therefore, the width of the given rectangle is 2x²-3x+3.
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find X and Y X - 3 y + 3 15 12
To solve this problem we have to remember that diagonals of a parallelogram bisect each other. This means that they intersect in the midle point of each other. From this we can conclude that
[tex]\begin{gathered} x-3=15 \\ \text{and} \\ y+3=12 \end{gathered}[/tex]Once we have our equations we can solve them. Let's find x
[tex]\begin{gathered} x-3=15 \\ x=15+3 \\ x=18 \end{gathered}[/tex]Now, let's find y
[tex]\begin{gathered} y+3=12 \\ y=12-3 \\ y=9 \end{gathered}[/tex]Then x=18 and y=9,