In order to find the interval of values where 95% of the shoe sizes lie, let's find the values of z-score that represents 2.5% to the left and 2.5% to the right of the standard distribution curve:
Looking at the z-table for the probabilities of 0.025 and 0.975, we have z1 = -1.96 and z2 = 1.96.
Now, we can calculate the values that define the interval using the formula below:
\(\begin{gathered} z=\frac{x-\mu}{\sigma} \\ -1.96=\frac{x-8.1}{1.47} \\ x-8.1=-2.88 \\ x=-2.88+8.1 \\ x=5.22 \\ \\ 1.96=\frac{x-8.1}{1.47} \\ x-8.1=2.88 \\ x=2.88+8.1 \\ x=10.98 \end{gathered}\)Therefore the correct option is the second one. (It's the only option with very close values to the ones calculated)
The seed and skin of a typical avocado is 35% of the avocado's weight. For an 8-ounce avocado, how many ounces of edible fruit does it have?
Answer: 5.2 edible fruit
Step-by-step explanation:
8 x .35 = 2.8. 8 - 2.8 = 5.2 edible fruit
Use the diagram shown. Solve for x. Find the angle measures to check your work. (Edit: nevermind i got the answer)
Answer:
x = 9
m<AOB = 29°
m<BOC = 57°
m<COD = 29°
Step-by-step explanation:
Given:
m<AOB = (4x - 7)°
m<BOC = (5x + 12)°
m<COD = (2x + 11)°
The diagram shows <AOB is congruent to <COD.
Set both angles equal to each other to find x.
m<AOB = m<COD
4x - 7 = 2x + 11
Collect like terms
4x - 2x = 7 + 11
2x = 18
Divide both sides by 2
2x/2 = 18/2
x = 9
Find the measure of each angle by plugging in the value of x into each expression for each angle:
m<AOB = (4x - 7)° = 4(9) - 7 = 36 - 7 = 29°
m<BOC = (5x + 12)° = 5(9) + 12 = 45 + 12 = 57°
m<COD = (2x + 11)° = 2(9) + 11 = 18 + 11 = 29°
What is the value of the expression below? (6) (6) (6) (6) O A. V6 O B. 6 C. 2/6 O D. 36
please help image attached!
Answer:
The unit circle centered at the origin in the Euclidean plane is defined by the equation:
\(x^2+y^2=1\\\)
Given an angle , there is a unique point P on the unit circle at an angle θ from the x-axis, and the x- and y-coordinates of P are:
\(x=cos \theta \\y = sin \theta\)
Consequently, from the equation for the unit circle:
\(cos^2\theta+sin^2\theta=1\)
the Pythagorean identity.
According to a recent poll, 27% of Americans get 30 minutes of exercise at least five days each week. Let's assume this
is the parameter value for the population. If a simple random sample of size were taken, what is the approximate
probability that , the proportion who exercise at least five days per week, is higher than 0.30?
The probability that the proportion of a sample is higher than 0.30 can be estimated using the Central Limit Theorem (CLT) which states that the distribution of the sample means approaches a normal distribution as the sample size increases. With a large sample size (n >= 30), we can use the normal distribution to approximate the distribution of the sample means.
Assuming the sample size is large, the standard error (SE) of the sample mean is given by
SE = sqrt(p * (1 - p) / n), where p is the population proportion (0.27) and n is the sample size.
With this information, we can find the Z-score corresponding to 0.30 using the formula: Z = (0.30 - 0.27) / SE
Since we don't know the sample size, we'll assume a conservative sample size of 30.
With a sample size of 30, the SE is approximately 0.039, and the Z-score is approximately 0.77.
Using a standard normal table, we can find the probability of a Z-score being greater than 0.77 is approximately 0.22.
Therefore, the approximate probability that the proportion who exercise at least five days per week is higher than 0.30 is 0.22.
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4. Use the table of values for a quadratic function to identify the following.
X
direction the graph opens:
-3
axis of symmetry:
vertex:
ON W
range:
y-intercept:
(as an ordered pair)
-3
-4
1
-3
x-intercepts:
(as ordered pairs)
2
3
4
interval of increase:
interval of decrease:
The numerical coefficient in -6x²y² is:
Answer:
-6 is the numeral cofficient
Three high school football teams each played four games. The Wildcats scored 18, 10, 14, and 18 points. The Knights scored 13, 17, 28, and 7 points. The Eagles scored 17, 28, 9, and 21 points. Which team had the highest mean points per game?
Answer:
The Eagles: 18.75
Step-by-step explanation:
The Mean of the wildcats: 15
The Mean of the Knights: 16.25
The Mean of the Eagles: 18.75
Ed is 7 years older than ted. Ed is also 3/2 times teds age. How old are ed and ted
Answer: Ted is 14 years old, Ed is 21 years old
Answer: Ted is 14 years old, and Ed is
21 years old.
Explanation is in the image.
Need help fast! Please help! Thank you.
Answer:
b
Step-by-step explanation:
Which of the following pairs show(s) two congruent triangles?
O B only
OB and C only
O A, B, and C
O A and C only
Answer:
B only
Step-by-step explanation:
Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.
Therefore, only B is correct
The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.
Explanation:The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.
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The polynomial function for this graph is of (odd,even, abnormal)
degree and the leading coefficient is (positive,negative,zero)
Answer:
first graph: The polynomial function for this graph is of ✔ odd degree and the leading coefficient is ✔ negative.
second graph: The polynomial function for this graph is of ✔ even degree and the leading coefficient is ✔ negative.
Step-by-step explanation:
hope this helped
When the output value of a real-valued function, f(x), is equal to f(-x), for all values of x inside the domain of f, the function is said to be an even function.
It is claimed that a real-valued function f(x) is an odd function when, for all values of x in the domain of f, the output value of f(-x) is equal to the negative of f(x).
Given:
As, we know the first graph graph of an odd function is at the same distance from the origin but in opposite directions and, graph of an even function remains the same after reflection about the y-axis.
So, The polynomial function for this graph is of odd degree and the leading coefficient is negative.
and, The polynomial function for this graph is of even degree and the leading coefficient is negative.
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Suppose that v varies directly with x, and v = 20 when x = 32.
A) Write a direct variation equation that relates x and y .
B) Find y when x = 24
\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{"v" varies directly with "x"}}{v = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} x=32\\ v=20 \end{cases} \\\\\\ 20=k(32)\implies \cfrac{20}{32}=k\implies \cfrac{5}{8}=k\hspace{8em}\boxed{v=\cfrac{5}{8}x} \\\\\\ \textit{when x = 24, what's v?}\qquad v=\cfrac{5}{8}(24)\implies v=15\)
How many times smaller is the value of 3 in 53075 than the 3 in 38499
Answer:
10 times smaller
Step-by-step explanation:
the first one the 3 is in the thousands place. in the second one, the 3 is in the ten thousands place.
A new cylindrical can with a diameter of 4cm is being designed by a local company. The surface area of the can is 140 square centimeters. What is the height of the can? Estimate using 3.14 for pi and round to the nearest hundredth. Apply the formula for the surface area of a cylinder SA=2B+Ph
The height of the can of cylinder shape is 9.14 cm.
What is a cylinder?
In mathematics, a cylinder is a three-dimensional solid that maintains two parallel bases separated by a curved surface at a specific distance. These bases frequently have a circular shape (like a circle), and an axis connects their respective centres.
We are given the diameter as 4 cm.
So, the radius is 2cm.
Also, it is given that the surface area of the can is 140 square centimeters.
So, using the surface area of cylinder, we get
⇒Area = 2πr (h + r)
⇒140 = 2π * 2 (h + 2)
⇒140 = 4π (h + 2)
⇒140 = 4 * 3.14 * (h + 2)
⇒140 = 12.56 * (h + 2)
⇒11.14 = h + 2
⇒h = 9.14
Hence, the height of the can of cylinder shape is 9.14 cm.
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i need help
can you look over this picture and see what the answer is
Answer:
AC = 12
Step-by-step explanation:
If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore
ΔABC is similar to ΔADE.
The sides of smaller triangle are in proportion with sides of bigger triangle.
Therefore we have the equation:
AC/AE = AB/AD
Substitute the given numbers:
x/x+15 =8/18
18x= 8(x+15)
18x = 8x+120
10x = 120
x = 12
AC=12
meow help me in math
Part (a)
Answer: 87------------------
Work Shown:
v = u + a*t
v = 7 + 10*8 ... plug in the given values
v = 7 + 80
v = 87
==================================================
Part (b)
Answer: 10------------------
Work Shown:
v = u + a*t
80 = 20 + 6*t .... plug in the given values
80-20 = 6t .... subtracting 20 from both sides
60 = 6t
6t = 60
t = 60/6 .... divide both sides by 6
t = 10
Answer:
first person is write
Step-by-step explanation:
A recipe says that 2 cups of dry rice will serve 6 people. How many cups of rice are needed to serve 45 people?
(Please Help)
Answer:
7.5 cups pf rice
Step-by-step explanation:
45 divided by 6
The elevation of a mountain is 6510 feet above sea level.
Write a signed number to represent this elevation.
Translate the given statement into a linear equation in the form
ax + by = c using the indicated variable names. Do not try to solve the resulting equation.
The number of new clients (x) is 149% of the number of old clients (y).
On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y
what is a sequence?A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.
The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:
x = 1.49y
-1.49y + x = 0
-149y + 100x = 0
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The linear equation in the required form is: x - 1.49y = 0
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b
Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."
Using this information, we can write:
x = 1.49y
To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.
Subtracting 1.49y from both sides, we get:
x - 1.49y = 0
So the linear equation in the required form is:
x - 1.49y = 0
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A number cube for a game has a volume of 64 mm3.
What is the length of one side of the cube?
A. 3.27 mm
B. 4 mm
C. 6.46 mm
D. 8 mm
(Please explain why)
Answer:
B. 4mm
Step-by-step explanation:
A cube is a 3d square, so the length, width, and height are equal. To find the volume you have to times all three of those things. 4^3 or 4 * 4 * 4, is 64.
Answer:
B is the answer ill come back if it's wrong
Update: Its correct
Step-by-step explanation:
Which angles are corresponding angles?
Check all that apply.
اله
5 1
7
6/2
8/4
3
A. 6 and 3
B. 1 and 6
C. 5 and 7
D. 7 and 2
E. 6 and 8
F. 1 and 3
The corresponding angles among the given options are:
B. 1 and 6
F. 1 and 3
Corresponding angles are angles that are in the same position at different intersections of lines when a transversal cuts through them. Checking the options given:
A. 6 and 3: These angles are not corresponding angles as they are not positioned in the same location at different intersections of lines.
B. 1 and 6: These angles are corresponding angles as they are both positioned in the same location at different intersections of lines.
C. 5 and 7: These angles are not corresponding angles as they are not positioned in the same location at different intersections of lines.
D. 7 and 2: These angles are not corresponding angles as they are not positioned in the same location at different intersections of lines.
E. 6 and 8: These angles are not corresponding angles as they are not positioned in the same location at different intersections of lines.
F. 1 and 3: These angles are corresponding angles as they are both positioned in the same location at different intersections of lines.
The corresponding angles among the given options are:
B. 1 and 6
F. 1 and 3
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Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions
that a randomly chosen student answered correctly. Here is the probability distribution of X along with
summary statistics:
0
1
2
2.
3
X = # correct
P(X)
0.05
0.20
0.50
0.25
Mean: Hex = 1.95
Standard deviation: Ox 0.8
Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give
every student 5 additional bonus points. Let Y represent a random student's score.
What are the mean and standard deviation of Y?
Hy =
points
Oy
points
Answer:
24.5 points
8 points
Step-by-step explanation:
khan academy
The mean is 1.95 and the standard deviation is 2.41 for the given distribution.
What is the standard deviation?A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.
The given data as :
Correct question (x) Probability
0 0.05
1 0.20
2 0.50
3 0.25
In this scenario, we must calculate the mean, which is the product of the correct question and the probability. The mean will then be subtracted from the correct question. multiply the difference between the correct question and the mean by probability. This indicates the pay variance. off's The standard deviation of the distribution is given by taking the square root of the variance of the correct question.
Mean = 0 × 0.05 + 1 × 0.20 + 2 × 0.50 + 3 × 0.25
Mean = 1.95
Variance = (0 - 1.95)² + (1 - 1.95)² + (2 - 1.95)² + (3 - 1.95)²
Variance = 3.8025 + 0.9025 + 0.0025 + 1.1025
Variance = 5.81
Standard deviation = √(Variance)
Standard deviation = √(5.81)
Standard deviation = 2.41
Thus, the mean is 1.95 and the standard deviation is 2.41 for the given distribution.
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Can somebody help me please.
Answer:
The correct answer is the last one: 8 x 16 = ?
Step-by-step explanation:
hope this helps. pls mark this as brainiest if im correct! Thx have a great day... :)
i need help with these 9 questions they’re pretty simple
Answer:
1. n = 4
2. n = -29
3. n = -28
4. n = -48
5. n = -22
6. n = 97
7. n = 220
8. n = -18
9. n = 36
Step-by-step explanation:
1. -n = -4
Multiply both by -1 to get n = 4
2. 12 + n = -17
Subtract 12 from both sides of the equation to get n = -29
3. -n/14 = 2
Multiply by 14 on both sides of the equation to get -n = 28
Multiply -1 on both sides of the equation to get n = -28
4. -42 = n + 6
Subtract 6 from both sides of the equation to get -48 = n or n = -48
5. -4n = 88
Divide -4 on both sides of the equation to get n = -22
6. n + -3 = 94
Add 3 to both sides of the equation to get n = 97
7. 11 = -n/-20
Multiply by -20 on both sides of the equation to get -220 = -n or -n = -220
Multiply -1 on both sides of the equation to get n = 220
8. -108 = 6n
Divide by 6 on both sides of the equation to get -18 = n or n = -28
9. 67 = 31 + n
Subtract 31 from both sides of the equation to get 36 = n or n = 36
I Hope That This Helps! :)
Tina wants to run 123 miles over
7 days. She wants to run the same
distance each day. How far must she
run each day?
Answer:
17 4/7
Step-by-step explanation:
we'll need to divide 123 by 7
123/7= 17 R 4
But she can't have an extra 4 miles out so,
17 4/7
Ben is walking 150 miles in 31 days to raise money for a charity. He wants to walk the same distance each day. How far should he walk each day?
Explain what you did with the remainder and why.
Paul and Kristen have planned a long hike. They will both travel the same route and will not stop. Paul starts two hours before Kristen. He walks three miles per hour and does not slow down or speed up. If Kristen walks four miles per hour, and does not slow down or walk faster, how many miles must she walk to catch up with Paul?
Answer:
Kristen should walk 12 miles to catch up with Paul
Step-by-step explanation:
Paul = 2hrs earlier
= walks at 3 miles per hour
= 3miles x 2 hrs = 6 miles
covers 6 miles at the time Kristen starts
Kristen = 4 miles per hour
Paul has a lead of 6 miles.
if Kristen walks another hour of 4 miles she would have covered 8 miles and Paul would have covered 9 miles and if Kristen were to cover one more hour,
Kristen would be at 12 and so would Paul.
Kristen should walk 12 miles to catch up with Paul
Find a fraction that, when multiplied by 1/3, is less than 2/7. Justify your answer.
Step-by-step explanation:
\(x < \frac{6}{7} \)
All the fractions which less than (6/7) will be true
The steps of the solution in the above photo
I hope that is useful for you :)
Answer:
1/2 times 1/3
Step-by-step explanation:
Multiply them and you get 1/6 which is less than 2/7.
please help it's due tomorrow
Answer:
B. -414,720 x⁷y⁶
Step-by-step explanation:
To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.
The binomial theorem states that for an expression of the form (a + b)ⁿ:
\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)
For the expression (2x - 3y²)¹⁰:
a = 2xb = -3y²n = 10Therefore, each term in the expression can be calculated using:
\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)
The 4th term is when r = 3. Therefore:
\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)
So the 4th term of the given expansion is:
\(\boxed{-414720\:x^7y^6}\)