Answer:
[tex] x = 8\sqrt{2} [/tex]
Step-by-step explanation:
Leg = x
Hypotenuse = 16
[tex] x\sqrt{2} = 16 [/tex]
[tex] x = \dfrac{16}{\sqrt{2}} [/tex]
[tex] x = \dfrac{16}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}} [/tex]
[tex] x = \dfrac{16\sqrt{2}}{2} [/tex]
[tex] x = 8\sqrt{2} [/tex]
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 421 gram setting. It is believed that the machine is underfilling the bags. A 43 bag sample had a mean of 414 grams. Assume the population standard deviation is known to be 19.
Required:
a. Is there sufficient evidence at the 0.1 level that the bags are underfilled?
b. Find the P-value of the test statistic.
Answer:
a) The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.
b) 0.0078.
Step-by-step explanation:
Question a:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 421 gram setting.
At the null hypothesis, it is tested if the mean is of 421, that is:
[tex]H_0: \mu = 421[/tex]
It is believed that the machine is underfilling the bags.
At the alternative hypothesis, it is tested if the mean is of less than 421, that is:
[tex]H_a: \mu < 421[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
421 is tested at the null hypothesis:
This means that [tex]\mu = 421[/tex]
A 43 bag sample had a mean of 414 grams. Assume the population standard deviation is known to be 19.
This means that [tex]n = 43, X = 414, \sigma = 19[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{414 - 421}{\frac{19}{\sqrt{43}}}[/tex]
[tex]z = -2.42[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean below 414, which is the p-value of z = -2.42.
Looking at the z-table, z = -2.42 has a p-value of 0.0078.
The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.
b. Find the P-value of the test statistic.
As found above, the p-value of the test statistic is 0.0078.
Find two consecutive even numbers whose sum is 758.
Answer:
378 and 380
Step-by-step explanation:
The two even consecutive numbers that add up to 758 are going to be very close to half of 758. This is because two half of 758 are going to be the most similar addends of 758. This is important because the answers will be consecutive and therefore, must also be very similar. To solve, first, divide 758 by 2. This is 379, which is not an even number. So, to find the needed addends subtract and add 1 to 379. Both of these will be even and consecutive. These two numbers are 378 and 380. Then, to check you, can add them and see that they do sum 758.
Answer:
Step-by-step explanation:
Let the first number = x
Let the second number = x + 2
x + x + 2 = 758 Collect like terms
2x + 2 = 758 Subtract 2
2x = 758 - 2 Combine
2x = 756 Divide by 2
2x/2 = 756/2
x = 378
The first number is 378
The second number 380
If your teacher is really fussy, you can do it this way.
Let the first number = 2x
Let the second number = 2x + 2
The reason for this is to guarantee that both numbers were even to start with.
2x + 2x+2 = 758 Combine like terms
4x + 2 = 758 Subtract 2
4x = 756 Divide by 4
x = 756/4
x = 189
Therefore 2x = 378
2x + 2 = 380 Just as before.
I need help guys thanks so much
Answer:
A. 243
Step-by-step explanation:
[tex] 81^\frac{5}{4} = (3^4)^\frac{5}{4} = 3^{4 \times \frac{5}{4}} = 3^5 = 243 [/tex]
Answer: A
I just simplified it to 3^5, and that is also 243.
Last question guys! Help help help
9514 1404 393
Answer:
slope 125, annual dues paymentStep-by-step explanation:
The two given points can be used to find the slope:
m = (y2 -y1)/(x2 -x1)
m = (650 -400)/(4 -2) = 250/2 = 125
The vertical axis is cost, and the horizontal axis is years, so the slope is the ratio of these: cost per year.
The slope of $125 per year is the yearly membership dues cost.
The graph of [tex]y = ax^2 + bx + c[/tex] is a parabola. The axis of symmetry is [tex]x = -b/2a[/tex]. What are the coordinates of the vertex?
The vertex can be written as:
(-b/2a, b^2/(4*a) - b^2/2a + c)
For a general parabola:
y = a*x^2 + b*x + c
We can write the vertex as:
(h, k)
The x-value of the vertex is the value of the axis of symmetry.
Then we have:
h = x = -b/2a
Now we need to find the y-value of the vertex.
To do that, we just replace the variable "x" by the x-value of the vertex in our equation, so we get:
k = y = a*(-b/2a)^2 + b*(-b/2a) + c
k = b^2/(4*a) - b^2/2a + c
Then the coordinates of the vertex are:
(h, k) = (-b/2a, b^2/(4*a) - b^2/2a + c)
If you want to read more:
https://brainly.com/question/24302770
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the binomial quadratic expressions with their factored form.
Answer:
x²-36 and (x-6)(x+6)
9x-1 and(3x-1)(3x+1)
4x² -16 and 4(x-2)(x+2)
Step-by-step explanation:
when you multiply(x+6)(x-6)
you get x²-36,this is known as difference of two squares ie (a+b)(a-b)=(a²-b²)=0
x(x-6)+6(x-6)
x²-6x+6x-36
x² -36
the second the same explanation as the first
for the third, multiply (x+2)(x-2) it will give x²-4
then multiply this by 4 which is = 4x² - 16
14 80 tiles of side 30cm were used to cover a counter top. Calculate the area of the counter top in square metres.
Answer:
Step-by-step explanation:
1,480 is a lot of tiles. Did you mean 80 tiles?
30 cm = 0.3 m
Area of one tile = 0.3² m² = 0.09 m²
Multiply the number of tiles by 0.09 m².
Jared works at a clothing store and is listening to a customer complain about a shirt he purchased that's damaged. Which behavior can Jared exhibit to show good communication skills with the customer? O a) Stopping the customer to quickly explain the store's return policy b) Repeating back what he has heard once the customer is done speaking Od Asking the customer how the shirt was damaged O d) Promising the customer a full refund even though it's against policy
Answer:
C
Step-by-step explanation:
in my point of view, my choice is C (asking the customer how the shirt was damaged) because when he finds out the reason why the shirt was damaged, he will explain whether or not that fault is in the store's return policy
another reason:
A) stopping the customers when they are talking, it's impolite behavior and i ensure that that customer will feel disatified.
B) i guess that customer doesnt waste of time because it
D) a full refund without finding the reason, i dont think it's a good idea
A researcher conducts an ANOVA analysis and reports no differences in average certification exam test scores for nurses identified as Baby Boomers, Millennials or Generation X. You would expect to see:
Answer:
"Type II error" is the right answer.
Step-by-step explanation:
A type II mistake would be that a fake null hypothesis also isn't rejected. It's also called false negatives.It happens whenever an investigator does not eliminate a truly wrong null hypothesis. Here quite a scientist determines that whenever it genuinely exists, that there's no substantial consequence.Thus the above is the right answer.
In the past, Alpha Corporation has not performed incoming quality control inspections but has taken the word of its vendors. However, Alpha has been having some unsatisfactory experience recently with the quality of purchased items and wants to set up sampling plans for the receiving department to use. For a particular component, X, Alpha has a lot tolerance percentage defective of 52 percent. Zenon Corporation, from which Alpha purchases this component, has an acceptable quality level in its production facility of 20 percent for component X. Alpha has a consumer's risk of 10 percent and Zenon has a producer's risk of 5 percent. a. When a shipment of Product X is received from Zenon Corporation, what sample size should the receiving department test
Answer:
The answer is "28"
Step-by-step explanation:
[tex](LTPD) = 52\%\\\\(AQL) = 20\%\\\\\to \frac{LTPD}{AQL} = \frac{52\%}{20\%}= 2.6\\\\[/tex]
The value of [tex]\frac{LTPD}{AQL} = 2.6[/tex] that value of [tex]\frac{LTPD}{AQL} = 2.618[/tex]
Acceptance number, [tex]c = 9[/tex]
Value of [tex]n\times AQL = 5.426[/tex]
Sample size [tex]n = n\times \frac{AQL}{AQL} =\frac{5.426}{20\%} = 27.13=28[/tex]
Which fraction is equivalent to 3/-5? Please help ASAP
Answer:
-3/5
Step-by-step explanation:
3/ -5 is also equal to -3/5 or - (3/5)
Choose all options that apply. Which of the following are antiviral medications commonly used to treat the flu? | a) Azelastine Oxymetazoline c) Zanamivir O d) Oseltamivir
What is the measure of angle BCD? 146° O 250 O 40° D o 140° 1490 c O 1550
Answer: I think the correct answer is 40 but I am not sure.
Step-by-step explanation:
Answer: 40
The angle measure of BCD is m∠BCD = 140°.
What is an interior angle?Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."
Given that a quadrilateral ABCD.
To find the angle measure of BCD,
first, we find the other interior angle with supplementary angles.
m∠DAB = 180 - 25 = 155°
m∠ABC = 180 - 146 = 34°
m∠ADC = 180 - 149 = 31°
And the total sum of the interior angles of a quadrilateral is 360°
So, m∠BCD = 360 - (34 + 31 + 155)
m∠BCD = 140°
Therefore, m∠BCD = 140°.
To learn more about the interior angles;
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In the diagram below, ΔABC ≅ ΔDEF. Complete the statement AB¯¯¯¯¯¯¯¯≅ __
A. BC
B. DF
C. FE
D. DE
Answer:
The answer would be D. DE
Step-by-step explanation:
same prob
Congruent triangles are exact same triangles, but they might be placed at different positions. The correct option is D.
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes the length of line segment AB, and so on for others).
Given that ΔABC ≅ ΔDEF. Therefore, the given sentence can be completed as AB ≅ ΔDE.
Hence, the side AB ≅ ΔDE
Learn more about Congruent Triangles:
https://brainly.com/question/16921692
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A farmer wants to build a rectangular fence to enclose a 144\ \textup{ft}^2 yard. If the yard is square, how many feet of fence will he need?
Answer:
12* 12 = 144
thus 4*12 = 48 feet of fence
Step-by-step explanation:
Mark is investing $8,000 in an account paying 5.5% interest compounded daily. What will Mark's account balance be in 6 years?
Picture is the answer
The sum of two numbers is -17. Their difference is 41. Find the numbers
Answer:
x = 12
y = -29
Step-by-step explanation:
Our given equations: x + y = -17 and x - y = 41
Solve for x and substitute.
x = -17 - y
(-17 - y) - y = 41
-17 - 2y = 41
2y = -58
y = -29
Solve for x using y
x + (-29) = -17
x = 12
There is a swimming pool which has a length of 15 m and a width of 12 m. There is a 2 m wide path around the pool. If the cost of the path is $5 per , what is the cost of the path? Use words, numbers, and/or symbols to justify your answer.
Answer:
15m+12m+15m+13m=54m
2m×12m=24m
A circular pizza has a diameter of 12 inches and is cut into 10 congruent slices. What is the area of each slice, to the nearest tenth?
Group of answer choices
14.4 straight pi inches squared
3.6 straight pi inches squared
2.4 straight pi inches squared
12.4 straight pi inches squared
[tex]\\ \sf\longmapsto Area=2\pi r[/tex]
[tex]\\ \sf\longmapsto Area=2(3.14)\times 6[/tex]
[tex]\\ \sf\longmapsto Area=2(18.84)[/tex]
[tex]\\ \sf\longmapsto Area=37.68in^2[/tex]
Now area of each slice
[tex]\\ \sf\longmapsto \dfrac{37.68}{12}[/tex]
[tex]\\ \sf\longmapsto 3.6in^2[/tex]
The area of each slice of the pizza will be 3.6π square inches. The correct option is B.
What is the area of the sector?The circle is defined as the locus of the point traces around a fixed point called the center and is equidistant from the out trace.
It is given that a circular pizza has a diameter of 12 inches and is cut into 10 congruent slices.
Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the area of the sector of the circle will be
Area = (θ/2π) πr²
angle = 2π/10
The area will be calculated as below:-
Area = (2π/10)/2π) πr²
Area = ( π x 6 x 6 ) / 10
Area = 3.6π square inches
Therefore, the area of each slice of the pizza will be 3.6π square inches. The correct option is B.
More about the area of the sector link is given below.
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Please answer this and show the work/explain.
2/7m - 1/7 = 3/14
what is twice the amount of 86
Answer:
172
Step-by-step explanation:
[tex]86[/tex] × 2 = 172
Given the following absolute value function find the range.
f(x) = |x + 5| -8
Range: [5,00)
Range: [-5,00)
Range: [-8,00)
Range: [8,00)
Answer:
Range is (-8,00)
Step-by-step explanation:
According to the graph of the rational function y equals 4 over the quantity x squared minus 4 end quantity which of the following statements is/are true? The function is even. The function is increasing for all values in the domain. There is a horizontal asymptote along the x-axis. I only I and II only I and III only I, II, and III
Using function concepts, it is found that the correct options are:
I and III only
--------------------------------
The function is:
[tex]y = \frac{4}{x^2 - 4}[/tex]
--------------------------------
Statement 1:
A function is even if: [tex]f(x) = f(-x)[/tex]
We have that:
[tex]f(x) = \frac{4}{x^2 - 4}[/tex]
[tex]f(-x) = \frac{4}{(-x)^2 - 4} = \frac{4}{x^2 - 4} = f(x)[/tex]
Since [tex]f(x) = f(-x)[/tex], the function is even, and the statement is true.
--------------------------------
Statement 2:
The function increases when: [tex]f^{\prime}(x) > 0[/tex]
The derivative is:
[tex]f^{\prime}(x) = \frac{-8x}{(x^2-4)^2}[/tex]
The denominator is always positive, but the numerator can be both positive/negative, which means that when the numerator is negative(x > 0), the derivative will be negative, thus the function will decrease and the statement is false.
--------------------------------
Statement 3:
A horizontal asymptote is given by:
[tex]y = \lim_{x \rightarrow \infty} f(x)[/tex]
In this question:
[tex]y = \lim_{x \rightarrow \infty} \frac{4}{x^2 - 4} = \frac{4}{\infty - 4} = \frac{4}{\infty} = 0[/tex]
y = 0 is the x-axis, thus, the statement is true, and the correct option is:
I and III only
A similar problem is given at https://brainly.com/question/23535769
Answer:
I and III
Step-by-step explanation:
Explain why this quadrilateral is not a parallelogram.
Answer:
because only two of it's sides are parallel
Answer:
In this quadrilateral, opposite sides are not parallel. So, this quadrilateral is not a parallelogram.
Step-by-step explanation:
In Parallelogram, opposite sides are parallel
If the product of a and cis negative, you subtract the factors of the product to arrive at c. True False
9514 1404 393
Answer:
false
Step-by-step explanation:
The statement is nonsense (false). Regardless of the sign of a product, subtraction plays no part in anything related to it.
Figure A is a scale image of figure B. Figure A maps to figure B with a scale factor of 2/3. What is the value of x?
9514 1404 393
Answer:
x = 7
Step-by-step explanation:
10.5 maps to x with a scale factor of 2/3:
x = 10.5 × 2/3
x = 7
I NEED HELP ASAP!!! convert 0.252525 to a fraction and convert 2.454545 to a fraction
Answer:
1. What is 0.252525 as a fraction?
0.252525 as a fraction equals 252525/1000000
2. 2.454545 as a fraction equals 2454545/1000000
Step-by-step explanation:
To write 0.252525 as a fraction you have to write 0.252525 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.252525 = 0.252525/1 = 2.52525/10 = 25.2525/100 = 252.525/1000 = 2525.25/10000 = 25252.5/100000 = 252525/1000000
And finally we have:
0.252525 as a fraction equals 252525/1000000
2. What is 2.454545 as a fraction?
To write 2.454545 as a fraction you have to write 2.454545 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
2.454545 = 2.454545/1 = 24.54545/10 = 245.4545/100 = 2454.545/1000 = 24545.45/10000 = 245454.5/100000 = 2454545/1000000
And finally we have:
2.454545 as a fraction equals 2454545/1000000
Thanks
The sum of first 'n' terms. Sn of a particular Arithmetic Progression is given by Sn=12n-2n^2. Find the first term and the common difference.
Answer:
d=-4 and a=10
Step-by-step explanation:
The sum of a arithmetic sequence is given by (n/2)*(2a+(n-1)d). Comparing coefficients with the given Sn, we have; a-d/2=12 and d/2=-2, d=-4 and a=10.
Question 3 of 10
Which angle in ABC has the largest measure?
2
С
A ZA
B. 8
C. 20
O O
D. Cannot be determined
Answer:
Option C
Angle C has the largest measure
Can anyone please help me with this ?
Answer:
6.7
Step-by-step explanation:
The formula for volume is V=lwh.
320=(6)(8)x
Solve.
320=48x
Divide both sides by 48.
6.6666666=x
Round to the nearest tenth.
x=6.7
I hope this helps!
pls ❤ and give brainliest pls
Answer:
6.7 =x
Step-by-step explanation:
The volume is given by
V = l*w*h
320 = 8*6*x
320 =48x
Divide each side by 48
320/48 = 48x/48
6.6666666 = x
Rounding to the nearest tenth
6.7 =x
