Answer:
9812.29
Step-by-step explanation:
Using the compound interest formula,
[tex]8500 \left(1+\frac{0.024}{4} \right)^{(6)(4)} \approx 9812.29[/tex]
A) In a hostel , 30% of the beds are vacant. There are 210 guest beds at the hostel currently. How many beds are there at the hostel?
B) The hostel plans to increase its bed capacity by 15% over the next year. What is the planned bed capacity at the hostel?
C) The jeweler is trying to determine which box has the greatest weight. A box of gold weighs 0.55 kilograms and a box of silver weighs 14/25 kilograms. Which box is heavier?
A. The number of beds that are at the hostel will be 700 beds.
B. The planned capacity will be 105 beds.
C. The box of silver is heavier.
How to illustrate the information?A. In a hostel , 30% of the beds are vacant and T
there are 210 guest beds at the hostel currently. The number of beds will be:
= 30% of x = 210
0.3x = 210
x = 210/0.3
x = 700
The number of beds is 700.
B. The planned capacity will be:
= 15% × 700
= 0.15 × 700
= 105 beds.
C. When the jeweler is trying to determine which box has the greatest weight and a box of gold weighs 0.55 kilograms and a box of silver weighs 14/25 kilograms. It should be noted that 14/25 = 0.56. Therefore, the silver is heavier.
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PLSSS HELP MEEE
Classify quadrilateral RSTV. Support your answer by showing calculations.
The given quadrilateral RSTV is a kite.
What are quadrilaterals?The following characteristics apply to quadrilaterals, which are polygons.
It has four sides and four vertices surrounding four angles.A quadrilateral's interior angles add up to 360 degrees.To classify the quadrilateral calculate the length of its sides using the distance formula given as follows:
[tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }[/tex]
In the given quadrilateral RSTV,
RS = [tex]\sqrt{(2 - (-5))^{2} + (6 - 7)^{2} }[/tex] = [tex]\sqrt{50 }[/tex]
RV = [tex]\sqrt{(-4 - (-5))^{2} + (0- 7)^{2} }[/tex] = [tex]\sqrt{50}[/tex]
ST = [tex]\sqrt{(5 - 2)^{2} + (-3- 6)^{2} } = \sqrt{90}[/tex]
VT = [tex]\sqrt{(-3 - 0)^{2} + (5- (-4))^{2} } = \sqrt{90}[/tex]
The two adjacent sides of the quadrilateral are equal i.e. RS = RV and ST = VT.
A kite is a quadrilateral with two pairs of sides that are both the same length and are next to one another.
Therefore, the quadrilateral is a kite.
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Consider the incomplete paragraph proof.
Given: P is a point on the perpendicular bisector, l, of MN.
Prove: PM = PN
Line l is a perpendicular bisector of line segment M N. It intersects line segment M N at point Q. Line l also contains point P.
Because of the unique line postulate, we can draw unique line segment PM. Using the definition of reflection, PM can be reflected over line l. By the definition of reflection, point P is the image of itself and point N is the image of ________. Because reflections preserve length, PM = PN.
From the unique line postulate, we can draw unique line segment PM and as we are given that P is a point on the perpendicular bisector I of MN, the proof below has shown that using the definition of reflection, point P is the image of itself and point N is the image of point M
How to Interpret the Perpendicular Bisector?We are given :
Point P is a point on the perpendicular bisector, l, of MN.
Now, we want to prove that PM = PN
A Reflection in transformation can be defined as the transformation in which the figure is the mirror image of the other figure. This means that every point is a mirror reflection of itself .
With the aid of the definition of reflection, we can form the statement that point P is the image of itself , and point N is the image of M .
The line l which is the perpendicular bisector of MN acts as a Line of symmetry or axis of reflection.
Finally, when talking about transformations, it is common knowledge that reflections preserve length which means that the required proof PM = PN will hold true
Therefore, we will conclude that point N is the image of M .
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A railroad crew can lay 7 miles of track each day. They need to lay 189 miles of track. The length L (in miles) that is left to lay after d days is given by the following L (d)=189-7d
The number of days it will take the crew to lay all the track is; 27 days
The number of miles of track the crew has left to lay after 18 days is; 65 miles
How to solve Algebraic Equations?
We are given the equation that represents the length L (in miles) that is left to lay after d days as;
L(d) = 189 - 7d
where;
L is length in miles
d is number of days
Thus, the number of days it will take to lay all the tracks is;
Number of days = 189/7
Number of days = 27 days
The length L (in miles) that is left to lay after 18 days is;
L= 189 - 7(18)
L= 189 - 126
L= 65 miles
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Complete question is;
A railroad crew can lay 7 miles of track each day. They need to lay 189 miles of track. The length, L (in miles), that is left to lay after d days is given by the following function. L(d) = 189 - 7d
(How many days will it take the crew to lay all the track?)
(How many miles of track does the crew have left to lay after 18 days?)
Please help,, Consider the sequence of steps to solve the equation: 5(x - 3) = 7x2 Step 1 ⇒ 10(x - 3) = 7x Step 2 ⇒ 10x - 30 = 7x Step 3 ⇒ 3x - 30 = 0 Step 4 ⇒ 3x = 30 Step 5 ⇒ x = 10 Identify the property of equality which yields Step 5.
Summary: The solution to the equation (x - 3)(x + 9) = -27 is x = 0 and x = -6.
What’s the correct answer answer now for brainlist better he right
Answer:
they filter the air coming into the body
a container holds 2300 ounces fruit punch. A factory places the fruit punch into 32-ounce bottles. How man full Bottles of fruit punch can the factory produce?
A container holds 2300 ounces fruit punch. A factory places the fruit punch into 32-ounce bottles, factory can produce 71 full bottles.
What is an ounce?The uncia, an ancient Roman unit of measurement, is the source of the ounce (/ans/), any of numerous possible measures of mass, weight, or volume.
Although it is frequently used outside of the Anglosphere, it is predominantly employed in the United States to measure packaged foods and food portions, postal items, the areal density of fabric and paper, boxing gloves, and other items.
Although the avoirdupois ounce is the standard unit of mass for most applications, the actual weight of precious metals like gold, silver, platinum, palladium, rhodium, etc. is measured in "troy ounces," which are equal to 31.1034768 g.
'Ounce' is also used in the following other contexts: A unit of measure for force is the ounce-force. A unit of volume is the fluid ounce.A multitude of distinct ounces measuring mass or volume have been employed historically by various trades at various times and in various countries.Solving the question,
[tex]\frac{2300}{32} = 71.875[/tex]
Thus, we can say that a factory can produce 71 full bottles.
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For the equations given below, which statement is true? − 3 x − 8 = 19 − 3 x − 2 = 25 A. The equations have the same solution because the second equation can be obtained by subtracting 6 from both sides of the first equation. B. The equations have the same solution because the second equation can be obtained by subtracting 19 from both sides of the first equation. C. The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation. D. The equations do not have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
The statement that are true about the equations − 3 x − 8 = 19 and − 3 x − 2 = 25 is that he equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
How can the true statements about the equations be found?From the first equation, we were given, − 3 x − 8 = 19
then if we add 6 to the both sides of the equation then we will have
− 3 x − 8 + 6 = 19 + 6
Then if we perform the simplification on this equation we have,
− 3 x − 2 = 25
Which is the given equation i.e the second equation, hence the statement in the third option is correct.
Therefore, option C is correct.
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Can you please answer
From the given picture we can see
A right triangle DEC, where
The side opposite to angle C, ED has a length of 12 feet
The hypotenuse DC has length x feet
To find the value of x, we will use the sine ratio
[tex]\begin{gathered} \sin 70=\frac{opposite}{\text{hypotenuse}} \\ \sin 70=\frac{DE}{DC} \end{gathered}[/tex]Since the opposite side DE = 12
Since the hypotenuse DC = x
36 muffins and uses 4 cups of almonds. What is the unit rate of muffins per cup of almonds that he is using?
The unit rate of muffins per cup of almonds that the baker is for every 9 muffins, he uses 1 cup of almonds.
What is the unit rate?The unit rate is the ratio of a variable against another variable.
The unit rate explains the quantity relationship between the number of muffins produced and the cups of almonds used by the baker.
For this situation, a cup of almonds can make 9 muffins.
The total number of muffins made = 36
The total number of cups of almonds used = 4
The ratio of muffins to cups of almonds = 36:4 or 9:1
The unit rate of muffins per cup = 9 (36/4)
Thus, the baker is producing 9 muffins per cup of almonds used.
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Last year cost 24500 today worth 14300 what is the percentage change
The most appropriate choice for percentage will be given by- Percentage change in cost = 37.09 %
What is percentage?
A number or ratio which can be expressed as just a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a portion per hundred. Per 100 is what the word percent means. The letter "%" stands for it. As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any subject have been calculated in terms of percentages in academics. Ram, for instance, scored 78% on his final exam. This rate is computed based on Ram's overall grade point average (GPA) across all subjects.
For example 2% means [tex]\frac{2}{100}[/tex].
Here,
Cost last year = 24500
Cost today = 14300
Change in cost = 24500 - 14300
= 10200
Percentage change in cost = [tex]\frac{10200}{24500} \times 100[/tex]
= 37.09 %
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What is 7,984 -9,151 =
An urn has 13 balls that are identical except that 6 are white and 7 are red. A sample of 7 is selected randomly without replacement.
What is the probability that exactly 5 are white and 2 are red?
What is the probability that at least 5 of the balls are white?
The probability that the exactly 5 are white and 2 are red is126/1716 and,
the probability that at least 5 of the balls are white is 133/1716
Given that:-
Total number of balls in the urn = 13
Number of white balls = 6
Number of red balls = 7
Number of randomly selected balls = 7
We have to find the probability that the exactly 5 are white and 2 are red and the probability that at least 5 of the balls are white.
Probability that exactly 5 balls are white and 2 are red, P(x = 5) = [tex]\frac{^6C_5*^7C_2}{^{13}C_7}[/tex] = 126/1716 = 21/286
We know that,
Probability that atleast 5 balls are white = P(x = 5) + P(x = 6)
We know that,
P(x = 6) = [tex]\frac{^6C_6*^7C_1}{^{13}C_7}[/tex] = 7/1716
Hence,
Probability that atleast 5 balls are white = 126/1716 + 7/1716 = 133/1716.
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f(x) = (x + 3)² - 2x² ; x = -12
Tiana deposited $60 in an account earning 10% interest compounded annually.
To the nearest cent, how much will she have in 3 years
Find the value of x so that f(x) is parallel to g(x)need answers right away
○ 44
○ 25
○ 42
○ 18
Reason:
The angles shown must add to 180 degrees if we want the top and bottom lines to be parallel. These angles are same side interior angles.
(x+4)+(3x) = 180
4x+4 = 180
4x = 180-4
4x = 176
x = 176/4
x = 44
Answer:
x=42because of 3x and f or g
The support arm, AB, is
perpendicular to a line tangent to this curve on a roller coaster at the point of tangency B.
The equation of the tangent line to the curve at B is 3x + 2y = 28.
Find the equation of the support arm, AB.
B(4,8)
Lines perpendicular to tangents to curves, at
the point of tangency, are referred to as “normals.”
Answer:
[tex]y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]
Step-by-step explanation:
The genera slope-intercept equation of a line is
y = mx + 8 where m is the slope and b the y-interecept
A perpendicular line will have a slope = -1/m ie the negative of reciprocal of the first line such that m x (-1/m ) = -1
The equation of the tangent line is
3x + 2y = 28.
1. Convert to slope-intercept form:
Subtract 3x from both sidesSo slope = -3/2
Reciprocal of -3/2 = -2/3
Negative of reciprocal = +2/3
Slope of a perpendicular line should be -1/3 and the resultant equation of the line(the support arm) should be:
y = (2/3)x + b
To calculate b for the complete line equation plug in the point B(4, 8) and solve for B
y = 8 when x = 4
=> 8 = (2/3)(4) + b
Switch sides: (does not change any signs)
8/3 + b = 8
Subtract 8/3 on both sides
b = 8 - 8/3
b = 24/3 - 8/3
b = 16/3
So equation of the support arm is
[tex]\boxed{y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]
i need help with this please:-))
When two lines are perpendicular, their slopes have the following relation:
[tex]m_1=\frac{-1}{m_2}[/tex]If we rewrite this expression, we have:
[tex]m_1\cdot m_2=-1[/tex]The product of each slope is equal to -1.
Therefore the correct option is the fourth one.
What is the image point of (0,5)(0,5) after the transformation r_{y=x}\circ R_{180^{\circ}}r y=x ∘R 180 ∘ ?
The image of the point is (0, -5) after applying the geometric transformation, the answer is (0, -5).
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The point is (0, 5)
As we know, the
The rule for the above transformation:
(x, y) → (-x, -y)
(0, 5) → (0, -5)
Thus, the image of the point is (0, -5) after applying the geometric transformation, the answer is (0, -5).
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Write an equation of the line that passes through P(0, 0) and is parallel to the line y=4x-7. Your answer should be written in slope-intercept
Answer:
[tex]y=4x[/tex]
Step-by-step explanation:
Slope-intercept form:
[tex]y=mx+b\\[/tex]
m is the slope
b is the y-intercept
Parallel lines have the same slope, therefore we know that our new line will have the slope m = 4.
Since the point is the origin (0,0) we also know that the y-intercept will be 0.
Using this information, write the equation of the line:
[tex]y=4x+0[/tex]
Simplify:
[tex]y=4x[/tex]
vertical
none
obtuse
complementary
adjacent
answer:
vertical
explanation:
vertical angles are angles opposite each other.
odd even or neitheer
how many mistakes i have explain it to me
Answer:
neitheroddoddevenevenneitherevenevenStep-by-step explanation:
You want to classify a number of functions as even, odd, or neither.
Even FunctionAn even function has a graph that is symmetrical about the y-axis. It has the characteristic that ...
f(x) = f(-x)
A polynomial function will be an even function if it consists entirely of even-degree terms. (A constant is degree zero, hence even degree.) A rational function will be an even function if it can be reduced to the ratio of even functions.
Odd FunctionAn odd function has a graph that is symmetrical about the origin. It has the characteristic that ...
f(x) = -f(-x)
A polynomial function will be an odd function if it consists entirely of odd-degree terms. A rational function will be an odd function if it reduces to the ratio of an even and an odd function.
NeitherA function is neither even nor odd if it does not have one of the symmetries mentioned above. A polynomial consisting of a mix of even- and odd-degree terms will be neither even nor odd.
1. (x³+4x²)/(7x²+1)This is the ratio of a "neither" function to an even function. It is neither even nor odd.
2. (2x⁴+8x³)/(x³+4x²)The ratio can be reduced to ...
[tex]\dfrac{2x^4+8x^3}{x^3+4x^2}=\dfrac{2x^3(x+4)}{x^2(x+4)}=2x[/tex]
This consists only of an odd-degree term. It is an odd function.
3. x³/(7x²+1)This is the ratio of an odd function to an even function. It is an odd function.
4. (4x²+7)/(7x⁸+3x²)This is the ratio of two even functions. It is an even function.
5. (2x³+8x²)/(x³+4x²)As in problem 2, the function can be reduced:
[tex]\dfrac{2x^3+8x^2}{x^3+4x^2}=\dfrac{2(x^3+4x^2)}{x^3+4x^2}=2[/tex]
It is an even (degree 0) function.
6. (x²-4)/(x-2)This is the ratio of an even function to a "neither" function. It is neither even nor odd.
The function reduces to x+2, which is neither even nor odd.
7. 1/(x²+9x⁶)This is the ratio of two even functions. It is an even function.
8. (4x³+2x)/(7x⁵+3x³)This is the ratio of two odd functions. It can be reduced to the ratio of two even functions, so it is an even function.
[tex]\dfrac{4x^3+2x}{7x^5+3x^3}=\dfrac{2x(2x^2+1)}{x^3(7x^2+3)}=\dfrac{4x^2+2}{7x^4+3x^2}[/tex]
Determine a, b, c ∈ N*, different two by two, so that: [tex]\frac{1}{a}+\frac{1}{b}+\frac{1}{c}[/tex] is an integer
Using a system of equations, a possible set of values for a, b and c such that it results in an integer number is given by:
a = 6, b = 3, c = 2.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.
In the context of this problem, the variables are the given ones of:
a, b and c.
An integer number is a number that has no decimal part, hence the easiest way to solve this is making the sum of 1.
Attributing a = 6, we have that:
[tex]\frac{1}{6} + \frac{1}{b} + \frac{1}{c} = 1[/tex]
[tex]\frac{1}{b} + \frac{1}{c} = \frac{5}{6}[/tex]
This is possible with these two fractions:
[tex]\frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6} = \frac{5}{6}[/tex]
Hence the other possible values are given by:
b = 2, c = 3.
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Three friends went together to pick apples. They picked a total of 5 1/2 baskets of apples. If each person took home an equal amount of the baskets how many baskets did each person get?
The most appropriate choice for fraction will be given by -
Each person get [tex]1\frac{5}{6}[/tex] baskets of apples.
What is fraction?
Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
Here,
Number of person = 3
Total baskets of apple picked = [tex]5\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex] baskets
Number of baskets each person got =
[tex]\frac{11}{2} \div 3\\\frac{11}{2} \times \frac{1}{3}\\\frac{11}{6}\\1\frac{5}{6}[/tex]
Each person got [tex]1\frac{5}{6}[/tex] baskets of apples
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A 7ft board is cut into 2 pieces. If one piece is x feet long, express the other length in terms of x
Answer:
7-x
Step-by-step explanation:
If one piece is x, and the whole is 7, the missing piece would be 7-x
Hope this helps :)
Find values for the variables so that the following matrices are equal.
Given:
[tex]\begin{bmatrix}{x} & {7y} \\ {z} & {20}\end{bmatrix}=\begin{bmatrix}{4} & {21} \\ {4} & {20}\end{bmatrix}[/tex]Let's find the values of the variables so that the matrices are equal.
To find the values of the variables, divide the values of the result by the corresponding values of the main matrix.
We have:
• x = 4
• 7y = 21
Divide both sides by 7:
7y/7 = 21/7
y = 3
• z = 4
[tex]\begin{gathered} \begin{bmatrix}{x=4} & {7y=21} \\ {z=4} & {20}\end{bmatrix} \\ \\ \begin{bmatrix}{4} & {7(3)} \\ {4} & {20}\end{bmatrix} \end{gathered}[/tex]Therefore, we have:
• x = 4
,• y = 3
,• z = 4
ANSWER:
• x = 4
,• y = 3
,• z = 4
How to solve these three questions?
Using the normal distribution, it is found that:
a) The sampling distribution is approximately normal, with mean 45 and standard deviation 4.
b) The answer is not dependent on the sample size, as the underlying distribution is normal.
c) 0.0001 = 0.01% probability that the average is less than half an hour.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.By the Central Limit Theorem, the sampling distribution of sample means of size n is approximately normal, with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]. If the underlying distribution is normal, there are no sample size restrictions, while if the underlying distribution is not normal, the Central Limit Theorem is only valid for sample sizes of 30 and greater.For this problem, the parameters are given as follows:
[tex]\mu = 45, \sigma = 12, n = 9[/tex]
Hence the standard error of the approximately normal sampling distribution of sample means of size 9 is:
s = 12/sqrt(9) = 12/3 = 4.
As stated in the problem, the underlying distribution is normal, hence this is not dependent on the sample size.
For item c, the probability is the p-value of Z when X = 30, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (30 - 45)/4
Z = -3.75
Z = -3.75 has a p-value of 0.0001.
Hence the probability is of 0.0001 = 0.01%.
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Mai and Priya play on the same basketball team. During basketball practice yesterday, Mai attempted 40 free throws and was successful on 25% of them. How many successful free throws did Mai make yesterday?
Next question
Yesterday, Priya successfully made 12 free throws. Today, she made 150% as many. How many successful free throws did Priya make today?
Answer:
Mai made 10 successful free throws yesterday.
(25%=1/4 40/4=10)
Today Priya made 18 successful free throws.
(150%=1 1/2 12/2=6 12+6=18)
Lmk if u didn't understand my explanation :')
mikala and joanna were each given $20 to spend on a trip mikala spent 3/4 of her money and jonna spent 3/5 of her money how much money did they spend together
Answer:
$27
Step-by-step explanation:
[tex] \frac{3}{4} (20) + \frac{3}{5} (20) = 15 + 12 = 27[/tex]
whowever does my online math homework will get 200 points it yr9 maths (grade 8) maths
Answer:
I hope the deadline hasn't passed!
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