Answer:
7 units, 8 units
Step-by-step explanation:
Apparently, the cross section of each prism is a rectangle 1 unit by 2 units. Hence the total length will be ...
(30 units³)/((1 unit)(2 units)) = 15 units
Two numbers that differ by 1 and have a sum of 15 are 7 and 8.
The lengths of the prisms are 7 units and 8 units.
An amount of $18,000 is borrowed for 13 years at 4% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be
paid back?
Use the calculator provided and round your answer to the nearest dollar
Answer:
Total amount to be paid back = $29971
Step-by-step explanation:
Formula used to calculate the final amount of the loan to be paid,
Total amount to be paid = [tex]P(1+\frac{r}{n})^{nt}[/tex]
Where P = Principal amount of loan taken
r = rate of interest
n = Number of compounding in a year
t = duration of investment
By substituting the values in the formula,
Total amount to be paid after loan maturity = [tex]18000(1+\frac{0.04}{1})^{13\times 1}[/tex]
= [tex]18000(1.04)^{13}[/tex]
= 18000(1.66507)
= $29971.32
≈ $29971
Total amount to be paid after loan maturity will be $29971.
a hat contains 2 red apples and 3 green apples. a bucket contains 7 red apples and 3 green apples. a container is selected at random and an apple is drawn out. what is the probability that it will be a red apple
Answer:
15
Step-by-step explanation:
SAT Scores Suppose that the mathematics SAT scores for high school seniors for a specific year have a mean of 456 and a standard deviation of 100 and are approximately normally distributed. If a subgroup of these high school seniors, those who are in the National Honor Society, is selected, would you expect the distribution of scores to have the same mean and standard deviation? Explain your answer.
Answer:
The distribution of scores would not have the same mean and standard deviation
Step-by-step explanation:
According to the given data we have the following:
mean=456
Standard deviation=100
mathematics SAT scores for high school seniors for a specific year have a mean of 456 and a standard deviation of 100 and are approximately normally distributed
Therefore, we can conclude that a subgroup of these high school seniors would not to be a perfect representation, hence, the distribution of scores would not have the same mean and standard deviation.
Which of the following is the rule for rotating the point with coordinates (x,y), 180° clockwise about the origin? A. (x,y)→(y,−x) B. (x,y)→(−y,−x) C. (x,y)→(y,x) D. (x,y)→(−x,−y)
Hey there! I'm happy to help!
If you reflect a point across the x-axis, you have (x,y)⇒(x,-y). If you reflect across the y-axis, you have (x,y)⇒(-x,y). A 180° rotation is the same thing as reflecting across both the x and y axes. This means that the rule for rotating the point with coordinates (x,y) 180° clockwise about the origin is D. (x,y)⇒ (-x,-y).
Have a wonderful day! :D
h(6)= ? I don't even know what the question is asking me to do
Answer:
h(6) = 8
Step-by-step explanation:
h(6) is find the value of the function when x=6
What is the y value ( the value of the blue line) when x=6
Go to x=6 and go up to the blue line
y =8
h(6) = 8
Answer:
8At X = 6 , h(X) = 8
plug the value of x
h (6) = 8
please see the attached picture..
Hope this helps...
Good luck on your assignment...
Rewrite the equation by completing the squares x^2-x-20
Answer: x = ¹/₂ ± √⁸¹
------------
2
Step-by-step explanation:
First write out the equation
x² - x - 20
Now we now write the equation by equating to 0
x² - x - 20 = 0
We now move 20 to the other side of the equation. So
x² - x = 20,
We now add to both side of the equation square of the half the coefficient of the (x) and not (x²) which is (1) . So, the equation now becomes
x² - x + ( ¹/₂ )² = 20 + ( ¹/₂ )²
x² - ( ¹/₂ )² = 20 + ¹/₄
( x - ¹/₂ )² = 20 + ¹/₄, we now resolve the right hand side expression into fraction
( x - ¹/₂ )² = ⁸¹/₄ when the LCM is made 4
Taking the square root of both side to remove the square,we now have
x - ¹/₂ = √⁸¹/₄
x - ¹/₂ = √⁸¹/₂
Therefore,
x = ¹/₂ ± √⁸¹
-----------
2
helppppppppppppppppsdss
Answer:
t = p * n
Step-by-step explanation:
* - multiplication
t is the total cost
in order to find total cost we need to multiple cost per mile on the number of miles so we will receive cost of all miles that we went
Answer:
[tex]\boxed{t=pn }[/tex]
Step-by-step explanation:
t is total cost
The formula is in terms of t (total cost).
p is price per mile
Suppose the price per mile is £60. For every mile he travelled, he has to pay £60.
n is the number of miles travelled.
For example, Carlos travelled 4 miles and the price per mile is £30.
[tex]t=30 \times 4\\t=120[/tex]
His total cost will be £120.
The average child will wear down 727 crayons by his or her tenth birthday find the number of boxes of 64 crayons this is equivalent to.round to the nearest tenth
Answer:
11.4
Step-by-step explanation:
You just need to divide this one.
727/64=11.3593
Answer:
11.4
Step-by-step explanation:
727/64=11.359375
We have to round to the nearest tenth so, it would be 11.4.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
PLEASE ANSWERRR The ordered pair for the standard equation 3y – 2x = 12 is: (0, 4). (0, -4). (6, 2). None of these choices are correct.
Answer:
(0, 4)
Step-by-step explanation:
3y - 2x = 12.
Check each one by substituting:
(0,4):
3(4) - 2(0) = 12
12 = 12. - so its this one.
The ordered pair (0, 4) is for the equation 3y - 2x = 12 and the ordered pairs (0, -4). (6, 2) does not satisfy the equation.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The equation:
3y - 2x = 12
Plug x = 0 and y = 4
3(4) - 2(0) = 12
12 = 12 (true)
SImilarly for checking the other ordered pairs.
Thus, the ordered pair (0, 4) is for the equation 3y - 2x = 12 and the ordered pairs (0, -4). (6, 2) does not satisfy the equation.
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What is the value of 3/4 increased by 2 1/6?
Answer:
2 11/12
Step-by-step explanation:
3/4 + 2 1/6
Add the fractions.
35/12
= 2 11/12
Answer:
[tex]2\frac{11}{12}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}+2\frac{1}{6}=\\\\\frac{18}{24}+2\frac{4}{24}=\\\\2\frac{22}{24}=\\\\2\frac{11}{12}[/tex]
MATH HELP ASAP :( Write a polynomial f(x) that satisfies the given conditions. Express the polynomial with the lowest possible leading positive integer coefficient. Polynomial of lowest degree with lowest possible integer coefficients, and with zeros 9-41 and 0 (multiplicity 2).
Answer:
[tex]f(x)=((x-9)^2+16)x^2[/tex]
[tex]f(x)=x^4-18x^3+97x^2[/tex]
Step-by-step explanation:
If you want to, I could add the explanation as well. Just notify me.
Something really important I want to note is that since 9-4i is a zero, then 9+4i must must also be a zero.
A new city Mayor would like to determine the proportion of community voters who are ages 18 to 20 years. He has heard it is 10%. To test this prediction, he surveys 1000 random community voters and found that 111 of them are aged 18 to 20. The following is the setup for this hypothesis test: H0:p=0.10 H0:p≠0.10 The p-value for this hypothesis test is 0.04. At the 5% significance level, should he reject or fail to reject the null hypothesis?
Answer: He should reject the null hypothesis.
Step-by-step explanation: When using P-Values to decide if you accept or not the alternative hypothesis, compare the p-value with the chosen significance level (α).
In the Mayor's survey:
p-value = 0.04
α = 5% or 0.05
If the p-value is less than α, reject the null hypothesis and accept the alternative. If p-value is greater than or equals α, fail to reject the null hypothesis and don't accept the alternative.
Analysing the Mayor's survey:
p-value = 0.04 < α = 0.05
In conclusion, the Mayor should reject the null hypothesis and accept that the proportion of voters who are aged 18 to 20 is not equal to 10%, i.e., accept the alternative hypothesis: [tex]H_{a}[/tex]: p≠0.10
5 (u + 1) -
7 = 3
3 (u - 1) + 2u
Correct Question:
5 (u + 1) - 7 = 3 (u - 1) + 2u.
Solve for u
Answer:
See explanation below
Step-by-step explanation:
In this given question, we are required to find u.
Given the equation:
5 (u + 1) - 7 = 3 (u - 1) + 2u
Required:
Solve for u
To find u, first simplify both sides individually.
Simply 5 (u + 1) - 7:
Expand the parenthesis:
5u + 5 - 7
Collect like terms:
5u - 2
Simplify 3 (u - 1) + 2u:
Expand the parenthesis:
3u - 3 + 2u
Collect like terms:
3u + 2u - 3
5u - 3
Bring both simplified equations together:
5u - 2 = 5u - 3
5u - 5u - 2 = -3
-2 = -3
Since -2 ≠ -3, there is no solution.
Therefore, we can say the equation is invalid.
Which transformation is needed to be used on x^2, to get the graph of f(x) = 2x2 - 12x + 22?
Select one:
O a. Shift right by 3 units, stretch vertically by a factor 2 and then shift upward by 13 units
O b. Shift left by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units
O c. Shift right by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units
O d. Shift right by 3 units and shift upwards by 4 units
Please I need help
Answer: A
Step-by-step explanation:
The required transformation is Shift left by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units. Hence option B is correct.
What is graph?The graph is a demonstration of curves which gives the relationship between x and y axis.
Since, both curve of x² and 2x² - 12x + 22 is in the graph.
Now, the steps of transformation of x² into 2x² - 12x + 22 is as follows.
1) Shift left by 3 units.
2) Stretch vertically by a factor 2.
3) Shift upward by 4 units
Thus, the required result will be seen graph.
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Help ASAP!!!
Find sin(c). Round to the nearest hundredth if necessary.
A: 0.38
B: 0.92
C:0.42
D:1.08
Answer:
The answer is option A
0.38Step-by-step explanation:
sin ∅ = opposite / hypotenuse
Since we are finding sin (c)
From the question
The opposite is BA
The hypotenuse is AC
So we have
sin c = BA/ AC
BA = 5
AC = 13
sin c = 5/13
sin c = 0.384615
sin (c) = 0.38 to the nearest hundredth
Hope this helps you
Answer:
[tex]\boxed{Sin C = 0.38}[/tex]
Step-by-step explanation:
Sin C = opposite/hypotenuse
Where opposite = 5, hypotenuse = 13
Sin C = 5/13
Sin C = 0.38
It is urgent plz answer
Answer:
my class is 8 th is I don't now this answer
In graphing a trigonometric function, how does one establish which are the EXTREMUM coordinates and which are the MIDLINE INTERCEPTION coordinates. I can find the x values and the y values but do not know which X goes with which Y and the graphs end up incorrect! It is EXTREMELY frustrating. How do I discern which is which!!!!! Thank You.
Answer:
If I getting the question correctly, your doubt is the order of the values you get after doing the math. I mean, you can do the calculations, but in the end, you don't form the coordinate pairs correctly, that's why I understand from your question. So, here is what you need to do.
One way to graph is by using the definitions of those kinds of functions. For example, let's say we want to find the points to draw the function: [tex]y=sin(x)[/tex]
Remember that trigonometric functions have a specific period, that means, their drawing repeats over and over again after a certain number. That period is [tex]2 \pi[/tex], that means this number represents a cycle.
So, the main thing you need to do is to pick a starting point to then, draw the curve according to the [tex]2 \pi[/tex] period.
Now, we know that sine functions intercept the origin of the coordinate system, as you can observe in the image attached, there you can see that from the origin you draw those waves making sure you intercept the x-axis at every [tex]\pi[/tex] number. In the end, you will have a sine function.
On the other hand, if you want to have a chart with all x-values and y-values. First, you need to set x-values: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Then, you need to find each y-values for each of them.
Now, you have to draw a chart value, to keep in other the coordinate pairs, that way, you'll have the correct pairs at the end.
For example, for [tex]x=-5[/tex], we get [tex]y=-0.09[/tex], that means in the chart value, you are gonna form the pair [tex](-5, -0.09)[/tex], and now you have your first point of the drawing. Then, you keep repeating the process until you complete all the chart values.
As you can imagine, you're going to get really small decimal numbers, that's why I explained to you the first method, it's faster and easier.
Tree diagram:
Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow. If he draws one of the pieces without looking, what is the probability of drawing the green before the red?
Answer: [tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.
We assume that repetition is not allowed
Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex] [By permuattaions]
[tex]=\dfrac{4\times3\times2}{2}=12[/tex]
Favourable outcome = First green then red (only one way)
So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{12}[/tex]
hence, the required probability =[tex]\dfrac{1}{12}[/tex]
What is the value of $\sqrt{36 \times \sqrt{16}}$?
Answer:
24
Step-by-step explanation:
If we have two square roots like [tex]\sqrt{36}\cdot\sqrt{16}[/tex], we could do this either of two ways.
1. Multiply 36 by 16 and find the square root of that
[tex]\sqrt{36\cdot16} = \sqrt{576} = 24[/tex]
2. Find the square root of both of them then multiply.
[tex]\sqrt{36} = 6, \sqrt{16} = 4, 6\cdot4 = 24[/tex]
Hope this helped!
In a random sample of 40 refrigerators, the mean repair cost was $150. Assume the population standard deviation is $15.50. Construct a 99% confidence interval for the population mean repair cost. Then change the sample size to n = 60. Which confidence interval has the better estimate?
Answer: ($143.69, $156.31)
Step-by-step explanation:
Confidence interval to estimate population mean :
[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\sigma[/tex] = population standard deviation
n= sample size
[tex]\overline{x}=[/tex] Sample mean
z= critical value.
As per given,
n= 40
[tex]\sigma[/tex] = $15.50
[tex]\overline{x}=[/tex] $150
Critical value for 99% confidence level = 2.576
Then, 99% confidence interval for the population mean:
[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]
Hence, the required confidence interval : ($143.69, $156.31)
The length of human pregnancies from conception to birth varies accordingly to a distribution that is approximately normal with mean 266 days and standard deviation 16 days. a study enrolls a random sample or 16 pregnant women. what are the mean and standard deviation of the sampling distribution of Xbar? What is the probability the average pregnancy length exceed 270 days?
Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) = 266 days, standard deviation (σ) = 16 days, sample size (n) = 16 women.
a) The mean of the sampling distribution of Xbar ([tex]\mu_x[/tex]) is given as:
[tex]\mu_x=\mu=266\ days[/tex]
The standard deviation of the sampling distribution of Xbar ([tex]\sigma_x[/tex]) is given as:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n} } =\frac{16}{\sqrt{16} }=4[/tex]
b) The z score is a measure in statistics used to determine by how much the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For x > 270 days:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{270-266}{\frac{16}{\sqrt{4} } }=1[/tex]
The probability the average pregnancy length exceed 270 days = P(x > 270) = P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587 = 15.87%
Which expression is equivalent to (x^1/2 y ^-1/4 z)^-2
Answer:
x^-1 y^½ z^-2
A mechanic earns $5 more per hour than his helper. On a six-hour job the two men earn a total of $114. How much does each earn per hour?
Answer:
Step-by-step explanation:
m= the amount of money the mechanic makes.
h= the amount of money the helper makes.
m=h+5
m+h=114
h+5+h=114
2h+5=114
h=54.50
m=59.5
Helper makes $9 an hour.
Mechanic makes $9.92 an hour.
The earning of helper each earn per hour is 7$ /hr.
To find earning of helper per hour.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and also the properties and manipulation of numbers.
Given that:
let the cost /per hour of helper be x
and that of the mechanic is x+5
now for 6 hour job total earning is
6(x+x+5) = 114
=> 2x+5 = 19
so, 2x = 14 or x = 7
the earning of helper is = 7$ /hr
and earning of mechanic is = 12$/hr
So, the earning of helper each earn per hour is 7$ /hr.
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The average weight of a person is 160.5 pounds with a standard deviation of 10.4 pounds. 1. What is the probability a person weighs more than 150.2 pounds
Answer:
0.8390
Step-by-step explanation:
From the question,
Z score = (Value-mean)/standard deviation
Z score = (150.2-160.5)/10.4
Z score = -0.9904.
P(x>Z) = 1- P(x<Z)
From the Z table,
P(x<Z) = 0.16099
Therefore,
P(x>Z) = 1-0.16099
P(x>Z) = 0.8390
Hence the probability that a person weighs more than 150.2 pounds = 0.8390
You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a tail AND an even number on the die AND a card less than 5 (assume the ace is equal to 1) from the deck?
[tex]|\Omega|=2\cdot6\cdot52=624\\|A|=1\cdot3\cdot16=48\\\\P(A)=\dfrac{48}{624}=\dfrac{1}{13}[/tex]
Answer:
1/13
Step-by-step explanation:
The result of a biology test was collected, and the grades and gender are summarized below A B C Total Male 5 4 17 26 Female 6 2 15 23 Total 11 6 32 49 Let p p represent the proportion of all female students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p p to three decimal places. Enter your answer as a tri-linear inequality using decimals (not percents).
Answer:
99.5% Confidence interval = (-0.025, 0.547)
= -0.025 < p < 0.547
Step-by-step explanation:
| A | B | C | Total
Male | 5 | 4 | 17 | 26
Female | 6 | 2 | 15 | 23
Total | 11 | 6 | 32 | 49
If p represent the proportion of all female students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.
All female students = 23
Female students that score an A = 6
p = (6/23) = 0.2608695652 = 0.261
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = (6/23) = 0.261
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 99.5% confidence interval for sample size of 23 is obtained from the t-tables since information on the population standard deviation is not known.
we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 23 - 1 = 22.
Significance level for 99.5% confidence interval
(100% - 99.5%)/2 = 0.25% = 0.0025
t (0.0025, 22) = 3.119 (from the t-tables)
Standard error of the mean = σₓ = √[p(1-p)/N]
p = 0.261
N = sample size = 23
σₓ = √(0.261×0.739/23) = 0.091575
99.5% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.261 ± (3.119 × 0.091575)
CI = 0.261 ± 0.2856
99.5% CI = (-0.0246, 0.5466)
99.5% Confidence interval = (-0.025, 0.547)
= -0.025 < p < 0.547
Hope this Helps!!!
Find the distance between the points X and Y shown in the figure.
Answer:
XY ≈ 14.87 units
Step-by-step explanation:
Calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = X(- 6, 3) and (x₂, y₂ ) = Y(8, - 2)
d = [tex]\sqrt{(8+6)^2+(-2-3)^2}[/tex]
= [tex]\sqrt{14^2+(-5)^2}[/tex]
= [tex]\sqrt{196+25}[/tex]
= [tex]\sqrt{221}[/tex]
≈ 14.87 ( to 2 dec. places )
A rectangle has a width of 3/4 inches and a length of 9/10 inches. Another rectangle
is larger but still proportional to the first rectangle. It has a width of 30 inches and a length of 36 what proportion could model this situation
Answer:
Bigger size / smaller size = 40
Step-by-step explanation:
Notice that we
36 / (9/10) = 30 / (3/4) = 40
Therefore the proportion model would be
Bigger size / smaller size = 40
Find the value of x. Give reasons to justify your solution. D ∈ AC
Answer:
x = 25°
Step-by-step explanation:
From the picture attached,
Since AE║BC and AC is a transverse,
Therefore, ∠EAC ≅ ∠BCA [Alternate interior angles]
m∠EAC = m∠BCA = x°
∠BCD = ∠DCB + ∠DBC [Since ∠BCD is an exterior angle of ΔBDC]
m∠BCD = m∠DCB + m∠DBC
50° = x° + x°
2x = 50
x = 25°
Therefore, value of x is 25°.
Answer: 25 degrees
Step-by-step explanation:
Which system type is a linear system with infinitely many solutions?
Answer:
down b3low
Step-by-step explanation:
The point where the two lines intersect is the only solution. An inconsistent system has no solution. Notice that the two lines are parallel and will never intersect. A dependent system has infinitely many solutions.