What is the value of x?
The square pyramid shown below has a base with sides of 10 units. The slant height of the pyramid is 8 units. What is the vertical height, h?
Round your answer to the nearest tenth.
Answer:
h = 6.2 units
Step-by-step explanation:
Given triangle ABC is a right triangle with the measures of the two sides,
BC = [tex]\frac{10}{2}[/tex] = 5 units
AC = 8 units
By applying Pythagoras theorem in the given triangle,
AC² = AB² + BC²
8² = AB² + 5²
AB² = 64 - 25
AB = √39
AB = 6.24 units
AB ≈ 6.2 units
14. In a statistics class with 15 males and 13 females, five students are selected to put problems on the board. What is the probability that:
a. 3 females and 2 males are selected? b.all five students selected are males? c. all five students selected are females? d.at least one male is selected?
Answer:
a) 0.3056 = 30.56% probability that 3 females and 2 males are selected.
b) 0.0306 = 3.06% probability that all five students selected are males.
c) 0.0131 = 1.31% probability that all five students selected are females.
d) 0.9869 = 98.69% probability that at least one male is selected.
Step-by-step explanation:
The students are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
15 + 13 = 28 students, which means that [tex]N = 28[/tex]
5 are selected, which means that [tex]n = 5[/tex]
13 females, which means that [tex]k = 13[/tex]
a. 3 females and 2 males are selected?
3 females, so this is P(X = 3).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,28,5,13) = \frac{C_{13,3}*C_{15,2}}{C_{28,5}} = 0.3056[/tex]
0.3056 = 30.56% probability that 3 females and 2 males are selected.
b.all five students selected are males?
0 females, so this is P(X = 0).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,28,5,13) = \frac{C_{13,0}*C_{15,5}}{C_{28,5}} = 0.0306[/tex]
0.0306 = 3.06% probability that all five students selected are males.
c. all five students selected are females?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,28,5,13) = \frac{C_{13,5}*C_{15,0}}{C_{28,5}} = 0.0131[/tex]
0.0131 = 1.31% probability that all five students selected are females.
d.at least one male is selected?
Less than five females, so:
[tex]P(X < 5) = 1 - P(X = 5) = 1 - 0.0131 = 0.9869[/tex]
0.9869 = 98.69% probability that at least one male is selected.
A paper factory makes cardboard sheets like the one shown below. If the area of each sheet is given by the expression 6x ^ 2 + 7x + 2, what are the dimensions of each sheet of cardboard?
Answer:
(3x+2) by (2x+1)
Step-by-step explanation:
A cardboard is a rectangle, and has two dimensions. Given a quadratic equation, you should find a way to split it in two.
The easiest way to do so is through factoring. (There are many ways to do this, take a look at the plethora of sources offered on the internet.)
When the expression 6x^2 + 7x + 2 is factored, it is (3x+2)(2x+1). Hence, these are your dimensions.
60 units needed, 14 units per case. What is the number of cases and the number of additional units?
Answer:
5 cases
10 additional units
Step-by-step explanation:
Given that :
Total number of units needed = 60 units
Total number of units per case = 14
Hence, the total number of cases required will be :
Number of units needed / number of units per case
Number of cases required = 60 / 14 = 4.285 (this means that 5 cases are required as 4 cases won't be up to 60 units)
With 5 cases, we have exceeded the required units needed :
Additional units will be : (14 * 5) - 60
Additional units = 70 - 60 = 10 units
Use the figure to find u.
Answer:
u = 2
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj side / hypotenuse
cos 45 = sqrt(2) / u
u cos 45 = sqrt(2)
u = sqrt(2) / cos 45
u = sqrt(2) / 1/ sqrt(2)
u = sqrt(2) * sqrt(2)
u =2
u=2
Answer:
Solution given:
Relationship between base and hypotenuse is given by cos angle.Cos 45°=base/hypotenuse
[tex]\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{u}[/tex]
doing crisscrossed multiplication
[tex]\sqrt{2}*\sqrt{2}=1*u[/tex]
u=2
Can someone help me solve this Please
9514 1404 393
Answer:
523 grams52 gramsStep-by-step explanation:
To find the initial amount, put 0 where t is in the formula and do the arithmetic.
A(0) = 523(1/2)^0 = 523(1) = 523
The initial amount is 523 grams.
__
To find the amount remaining after 100 years, put 100 where t is in the formula and do the arithmetic.
A(100) = 523(1/2)^(100/30) ≈ 523(0.0992123) ≈ 52
About 52 grams will remain after 100 years.
F(4) =
If g(x) = 2, x=
An
Step-by-step explon:
help with numer 5 please. thank you
Answer:
See Below.
Step-by-step explanation:
We are given that:
[tex]\displaystyle I = I_0 e^{-kt}[/tex]
Where I₀ and k are constants.
And we want to prove that:
[tex]\displaystyle \frac{dI}{dt}+kI=0[/tex]
From the original equation, take the derivative of both sides with respect to t. Hence:
[tex]\displaystyle \frac{d}{dt}\left[I\right] = \frac{d}{dt}\left[I_0e^{-kt}\right][/tex]
Differentiate. Since I₀ is a constant:
[tex]\displaystyle \frac{dI}{dt} = I_0\left(\frac{d}{dt}\left[ e^{-kt}\right]\right)[/tex]
Using the chain rule:
[tex]\displaystyle \frac{dI}{dt} = I_0\left(-ke^{-kt}\right) = -kI_0e^{-kt}[/tex]
We have:
[tex]\displaystyle \frac{dI}{dt}+kI=0[/tex]
Substitute:
[tex]\displaystyle \left(-kI_0e^{-kt}\right) + k\left(I_0e^{-kt}\right) = 0[/tex]
Distribute and simplify:
[tex]\displaystyle -kI_0e^{-kt} + kI_0e^{-kt} = 0 \stackrel{\checkmark}{=}0[/tex]
Hence proven.
A human resources office is working to implement an increase in starting salaries for new
administrative secretaries and faculty at a community college. An administrative secretary
starts at $28,000 and new faculty receive $40,000. The college would like to determine the
percentage increase to allocate to each group, given that the college will be hiring 8
secretaries and 7 faculty in the upcoming academic year. The college has at most $5,000 to
put towards raises. What should the percentage increase be for each group?
Answer:
Step-by-step explanation :
Let % increase in administrative secretary be = x
Let % increase in new faculty receive be = y
Administrative secretary salary = 28,000
New faculty receive Salary = 40,000
(8)*(x/100)* (28000) + (7)*(y/100)*(40000) = 5,000
2240x +2800 y = 5,000
224x +280 y = 500
56x +70y = 125
Therefore, x and y should be chosen such that it satisfy the above equation.
help with b please. thank you
Answer:
See explanation.
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringAlgebra II
Polynomial Long DivisionPre-Calculus
ParametricsCalculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Parametric Differentiation: [tex]\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle x = 2t - \frac{1}{t}[/tex]
[tex]\displaystyle y = t + \frac{4}{t}[/tex]
Step 2: Find Derivative
[x] Differentiate [Basic Power Rule and Quotient Rule]: [tex]\displaystyle \frac{dx}{dt} = 2 + \frac{1}{t^2}[/tex][y] Differentiate [Basic Power Rule and Quotient Rule]: [tex]\displaystyle \frac{dy}{dt} = 1 - \frac{4}{t^2}[/tex]Substitute in variables [Parametric Derivative]: [tex]\displaystyle \frac{dy}{dx} = \frac{1 - \frac{4}{t^2}}{2 + \frac{1}{t^2}}[/tex][Parametric Derivative] Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{t^2 - 4}{2t^2 + 1}[/tex][Parametric Derivative] Polynomial Long Division: [tex]\displaystyle \frac{dy}{dx} = \frac{1}{2} - \frac{7}{2(2t^2 - 1)}[/tex] [Parametric Derivative] Factor: [tex]\displaystyle \frac{dy}{dx} = \frac{1}{2} \bigg( 1 - \frac{9}{2t^2 + 1} \bigg)[/tex]Here we see that if we increase our values for t, our derivative would get closer and closer to 0.5 but never actually reaching it. Another way to approach it is to take the limit of the derivative as t approaches to infinity. Hence [tex]\displaystyle \frac{dy}{dx} < \frac{1}{2}[/tex].
Topic: AP Calculus BC (Calculus I + II)
Unit: Parametrics
Book: College Calculus 10e
I need help I don’t understand at all ?
Answer:
i think its the 3 line. they are congruent.
Answer:
its the 3rd option
Step-by-step explanation:
first of all AA means angle-angle which means we are using their angles to compare them
second, those lines on the sides are only there to tell you they are in the exact same angle, and the two boxes on the bottom show that the angle of both triangles is 90° therefore they are the same
PLEASE HELPPP THIS IS DUE ASAPPPP!!!!!!!!!!!!!! WILL GIVE BRAINLIEST
Answer:
I think the answer is 5/6
Step-by-step explanation:
There are three even numbers and two uneven numbers less than four. Therefore, on a standard die, the.probability of Rollin a number that is even or less than for is 5/6.
Help with solving this Functions problem
Answer:
See answers below
Step-by-step explanation:
Given the following functions:
r(x) = x - 6
s(x) = 2x²
r(s(x)) = r(2x²)
Replacing x with 2x² in r(x) will give;
r(2x²) = 2x² - 6
r(s(x)) = 2x² - 6
(r-s)(x) = r(x) - s(x)
(r-s)(x) = x - 6 - 2x²
Rearrange
(r-s)(x) = - 2x²+x-6
(r+s)(x) = r(x) + s(x)
(r-s)(x) = x - 6 + 2x²
Rearrange
(r-s)(x) = 2x²+x-6
A machine in a factory must be repaired if it produces more than 10% defectives in production. A random sample of 100 items from a day's production contains 15 defectives, and the foreman says that the machine must be repaired. Statistically, does the sample evidence support his decision to repair at the 0.01 significance level? Conduct a test by using both the critical region method and the p-value method.
From the test the person wants, and the sample data, we build the test hypothesis, find the test statistic, and use this to reach a conclusion both using the critical value and the p-value.
Doing this, the conclusions are:
The test statistic is [tex]z = 1.67 < z_c[/tex], meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.The p-value of the test is 0.0475 > 0.01, meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.---------------------------------------------------------
Hypothesis:
A machine in a factory must be repaired if it produces more than 10% defectives in production.
At the null hypothesis, we test if it does not have to be repaired, that is, the proportion is of at most 10%. So
[tex]H_0: p \leq 0.1[/tex]
At the alternative hypothesis, we test if it does have to be repaired, that is, the proportion is greater than 10%. So
[tex]H_1: p > 0.1[/tex]
------------------------------------------------------
Decision rule:
0.01 significance level, using a left-tailed test(testing if the mean is more than a value), which means that:
The critical value is Z with a p-value of 1 - 0.01 = 0.99, so [tex]Z_c = 2.327[/tex]. If the test statistic z is less than this, there is not enough evidence to reject the null hypothesis, that the proportion is of at most 10%, otherwise, there is.The p-value is the probability of finding a sample proportion above the one found. If it is more than 0.01, there is not enough evidence to reject the null hypothesis, otherwise, there is.----------------------------------------------------------
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.
0.1 is tested at the null hypothesis:
This means that [tex]\mu = 0.1, \sigma = \sqrt{0.1*0.9}[/tex]
A random sample of 100 items from a day's production contains 15 defectives.
This means that [tex]n = 100, X = \frac{15}{100} = 0.15[/tex]
Value of the test-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.15 - 0.1}{\frac{\sqrt{0.1*0.9}}{\sqrt{100}}}[/tex]
[tex]z = 1.67[/tex]
----------------------------------------------
Decision: Critical region
The test statistic is [tex]z = 1.67 < z_c[/tex], meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.
Decision: p-value
The p-value of the test is the probability of finding a sample proportion above 0.15, which is 1 subtracted by the p-value of z = 1.67.
Looking at the z-table, z = 1.67 has a p-value of 0.9525.
1 - 0.9525 = 0.0475.
The p-value of the test is 0.0475 > 0.01, meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.
A similar problem is found at https://brainly.com/question/24326664
5(6t-3)=5t+35
find the value of t
Answer:
t = 2
Step-by-step explanation:
5(6t-3)=5t+35
Step 1 distribute the 5 by multiplying 5 to what is inside of the parenthesis
5(6t) - 5(3) = 5t + 35
Outcome: 30t - 15 = 5t + 35
Step 2 add 15 to both sides
30t - 15 + 15 = 5t + 35 + 15
Outcome: 30t = 5t + 50
Step 3 subtract 5t from both sides
30t - 5t = 5t - 5t + 50
Outcome: 25t = 50
Step 4 divide both sides by 25
25t/25 = 50 we're left with t = 2
Ryan bought coco powder, sugar, and wheat flour. The cost of sugar is $3
lesser than 2 times the cost of coco powder, and the white flour is $2 more
than į of the cost of coco powder. The total cost is $22.56. Find the cost of
each item (Estimate to the nearest tenths place).
Answer:
A
Step-by-step explanation:
Because it’s correct, and explains the property correctly
PLEASE HELP ME ASAP!!!
The answer is 4 because the frequency is the number of cycles completed in one interval. Typically, the interval given is 2π. Here, you can count the cycles and get 4.
If the total income generated from Gasoline for AER was $408 millions, how much would be the cost for a barrel of gasoline
Please please help me i can’t figure this out .. ernest's friend rolls a six-sided number cube and lands on square 8. She asks Ernest to guess what number she rolled. He guesses that she rolled a 3. She says he's wrong.
ernest wonders if she could have rolled a number other than 3. Use a mapping diagram to help guess what number she rolled.
If she would have rolled
Create a Mapping Diagram
When playing this game, the square you land on during the first turn depends on the number you roll. You can write this as a function: SQUARE(number), or S(n). For example, if you roll a 2, you end up on square 2 (when you land on 3 you move back a space). So S(2) = 2.
1. Describe the possible inputs of S(n) using words. (2 points: 1 point for the description, 1 point for the list of numbers)
2. Describe the possible outputs of S(n) using words. (1 point)
3. Draw a mapping diagram for S(n) that maps all the possible inputs and outputs for a player's first turn. Note that the player should begin on square 1. (6 points: 3 points for the inputs and outputs, and 3 points for the mapping)
4. In the mapping diagram you created, what numbers are in the domain of S(n)? Explain what this means. (2 points: 1 point for the domain, 1 point for the explanation)
5. What numbers are in the range of S(n)? Explain what this means. (2 points: 1 point for the range, 1 point for the explanation)
Evaluate the Conjecture
6. Based on the mapping diagram, is it possible that the player rolled a number other than 3 to land on square 8? If so, which number or numbers? Explain your answer. (2 points: 1 point for the answer, and 1 point for the explanation)
Defining Functions
7. Does the mapping diagram you created for S(n) for the first turn of the game represent a function? Why or why not? (2 points: 1 point for the answer, and 1 point for the explanation)
Step-by-step explanation:
1. The inputs are the dice values. Since the cube is six sided, the possible. values are (1,2,3,4,5,6).
2. The outputs values are points if we roll the number. If we land in a special space, we must respect that rule so our outputs are
(2,2,8,5,6,8).
3. I cant show a mapping diagram on brainly. Draw a mapping diagram and make sure to connect the x values and y values of the following.Also make sure to start on square 1.
1 corresponds with 22 corresponds with 23 corresponds with 84 corresponds with 55 corresponds with 66 corresponds with 84. The domain of the function is the same as the input. The dice values, 1,2,3,4,5,6
5.The range are the. values that occur if we roll the number about square 1.
2,2,8,5,6,8
6. No, the player could have rolled 3 and landed on 8. The player also could have rolled 6.
7. Yes, every one x value corresponds with one y value.
For any event, P(A) + P(not A) =
Explanation:
P(A) represents the probability of event A
P(not A) is the probability that event A doesn't happen
We only have two choices: Either A happens or it doesn't
So that means P(A) + P(not A) = 1
The "1" represents a 100% chance, aka certainty.
Solve the following equation by first writing the equation in the form a x squared = c:
3 a squared minus 21 = 27
A. a = 4
B. a = plus-or-minus 4
C. a = plus-or-minus 16
D. a = 16
9514 1404 393
Answer:
B. a = plus-or-minus 4
Step-by-step explanation:
3a² -21 = 27 . . . . . . . given
3a² = 48 . . . . . . . . . . add 21 to both sides (desired form)
a² = 16 . . . . . . . . . . . divide both sides by 3
a = ±4 . . . . . . . take the square root
Test for symmetry and then graph the polar equation.
r=3−5sinθ
Answer:
Symmetric with respect to the x-axis
Symmetric with respect to the y-axis
Symmetric with respect to the origin
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
VW = 4.9
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 46°
Hypothenus = VU = 7
Adjacent = VW =?
The value of VW can be obtained by using the cosine ratio as illustrated below:
Cos θ = Adjacent / Hypothenus
Cos 46 = VW / 7
Cross multiply
VW = 7 × Cos 46
VW = 4.9
Therefore, the value of VW is 4.9
what's the radius of 16x^2+16y^2=1 With a center of (0,0) ?
Answer:
The center is (0,0) and the radius is 1/4
Step-by-step explanation:
The formula for a circle is
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
16x^2+16y^2=1
Divide by 16
x^2+y^2=1/16
x^2 + y^2 = (1/4) ^2
(x-0)^2 + (y-0)^2 = (1/4) ^2
The center is (0,0) and the radius is 1/4
In a poll, adults in a region were asked about their online vs. in-store clothes shopping. One finding was that % of respondents never clothes-shop online. Find and interpret a % confidence interval for the proportion of all adults in the region who never clothes-shop online.
The question is incomplete. The complete question is :
In a poll, 1100 adults in a region were asked about their online vs. in-store clothes shopping. One finding was that 43% of respondents never clothes-shop online. Find and interpret a 95% confidence interval for the proportion of all adults in the region who never clothes-shop online.
Solution :
95% confidence interval for p is :
[tex]$\hat p - Z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}} < p < \hat p + Z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}$[/tex]
[tex]$0.43 - 1.96\times \sqrt{\frac{0.43(1-0.43)}{1100}} < p < 0.43 + 1.96\times \sqrt{\frac{0.43(1-0.43)}{1100}}$[/tex]
0.401 < p < 0.459
Therefore, 95% confidence interval is from 0.401 to 0.459
Jeff has 20 coins. 2/5 of them are quarters. How many quarters does he have? How many coins are not quarters?
6 in.
what is the area of the rhombus
? in..?
6 in.
6 in. 15.5 in.
6 in.
Answer:
the area of rombus is produt of diagonals divide by 2
write your answer in simplest radical form
Answer:
s = 7√6.
Step-by-step explanation:
From the 30-60-90 triangle we know that cos 30 = √3/2.
cos 30 = s / 14√2
√3/2 = s / 14√2
2s = 14√2√3
s = 14√2√3 / 2
s = 7√6.
Suppose the amount of protein is at least 8.6 grams. What is the probability that it is more than 8.7 grams
This question is incomplete, the complete question is;
Many people grab a granola bar for breakfast or for a snack to make it through the afternoon slump at work. A Kashi GoLean Crisp Chocolate Caramel bar weighs 45 grams. The mean amount of protein in each bar is 8 grams. Suppose the amount of protein in the bars have a normal distribution with a standard deviation of 0.32 grams and a random Kashi bar is selected.
Suppose the amount of protein is at least 8.6 grams. What is the probability that it is more than 8.7 grams
Answer:
the required probability is 0.472
Step-by-step explanation:
Given the data in the question;
Let x represent the random variable that shows the protein in the bar.
{ normal distribution }
mean μ = 8
standard deviation σ = 0.32
Now, Suppose the amount of protein is at least 8.6 grams. What is the probability that it is more than 8.7 grams
first we get the z-score for x = 8.6
z = x - μ / σ
z = ( 8.6 - 8 ) / 0.32
z = 0.6 / 0.32
z = 1.875
so
P( x ≥ 8.6 ) = P( z ≥ 1.875 ) = 1 - 0.9696 = 0.0304
Also for, x = 8.7
z = x - μ / σ
z = ( 8.7 - 8 ) / 0.32
z = 0.7 / 0.32
z = 2.1875
so
P( x > 8.7 ∩ x ≥ 8.6 ) = P( x > 8.7 ) = P( z > 2.1875 ) = 1 - 0.98565 = 0.01435
Now, the required probability will be;
P( x > 8.7 | x ≥ 8.6 ) = [P( x > 8.7 ∩ x ≥ 8.6 )] / [ P( x ≥ 8.6 ) ]
= 0.01435 / 0.0304
= 0.472
Therefore, the required probability is 0.472
