On solving the provided question, by multiplying the give polynomials, we got to know that - [tex]( 3x^2 - 5x + 7) X (2x^2 + 6x - 4)[/tex] = [tex]6x^4 + 8x^3 - 28x^2 + 62x - 28[/tex], the coefficient of x3 is 8
what are polynomials?An mathematical expression known as a polynomial requires that all of the variables' exponents be integers. Each polynomial variable's exponent must be an integer that is not negative. Although a polynomial is made up of a constant and a variable, it cannot be divided by a variable.
Given polynomials are -
[tex]( 3x^2 - 5x + 7) and (2x^2 + 6x - 4)[/tex]
By multiply the given polynomials, we got -
[tex]( 3x^2 - 5x + 7) X (2x^2 + 6x - 4)[/tex]
= [tex]6x^4 + 8x^3 - 28x^2 + 62x - 28[/tex]
So, the coefficient of x3 is 8
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A vacant lot is assessed at $36,000. What property tax must be paid on the lot if the tax rate is 2.4 cents per $1? PLEASE SHOW WORK
Answer:
The property tax that must be paid on the lot is $864.
Step-by-step explanation:
The assessment value of the lot is $36,000, and the tax rate is 2.4 cents per $1, or 0.024. So the total amount of tax due is calculated as follows:
$36,000 * 0.024 = $<<36000*0.024=864>>864
Which of the following differential equation is exact?
A. (y2+ x)dx+ (y3 + x)dy = 0
B. (x + y) (dx - dy) = dx + dy
C. 2xydx + (x + y2) dy = 0
D. None of the above
Answer:
B
Step-by-step explanation:
Solve (x + y(x)) (-(dy(x))/(dx) + 1) = (dy(x))/(dx) + 1:
Let v(x) = x + y(x), which gives (dv(x))/(dx) = (dy(x))/(dx) + 1:
(-(dv(x))/(dx) + 2) v(x) = (dv(x))/(dx)
Simplify:
-((dv(x))/(dx) - 2) v(x) = (dv(x))/(dx)
Solve for (dv(x))/(dx):
(dv(x))/(dx) = (2 v(x))/(v(x) + 1)
Divide both sides by v(x)/(v(x) + 1):
((dv(x))/(dx) (v(x) + 1))/v(x) = 2
Integrate both sides with respect to x:
integral((dv(x))/(dx) (v(x) + 1))/v(x) dx = integral2dx
Evaluate the integrals:
log(v(x)) + v(x) = 2 x + c_1, where c_1 is an arbitrary constant.
Solve for v(x):
v(x) = W(e^(2 x + c_1))
Simplify the arbitrary constants:
v(x) = W(c_1 e^(2 x))
Substitute back for y(x) = -x + v(x):
Answer: y(x) = -x + W(c_1 e^(2 x))
How do I put this answer as a point?
5x - 4y = 11
x = 3
Answer:
(3,1)
Step-by-step explanation:
hii ! for this question, x = 3, which is your first point. for the second part, you're going to need to plug x into the 5x.
5(3)-4y=11
15-4y=11
subtract 15 from each side
-4y=-4
y=1
(3,1) is gonna be your answer !
A cake decorator mixed 3 cups of red frosting with 7 cups of blue frosting to make a purple frosting. Which ratio of cups of red frosting to cups of blue frosting will make the same shade of purple frosting?
Answer: 3 to 10. will be the ratio.
Step-by-step explanation:
the given set is a basis for a subspace w. use the gram-schmidt process to produce an orthogonal basis for w.
y₁ = [1 -4 0 1] and y₂ = [5 1 -6 -1] is the orthogonal basis for w using Gram-Schmidt process.
Given,
The set;
x₁ = [1 -4 0 1]
x₂ = [7 -7 -6 1]
We have to produce the orthogonal basis for w using the Gram-Schmidt process;
Here,
y₁ = x₁ = [1 -4 0 1]
Now,
Solve for y₂
y₂ = x₂ - [x₂y₁ / y₁y₁] y₁
That is,
y₂ = [7 -7 -6 1] - ( [7 -7 -6 1] [1 -4 0 1] / [1 -4 0 1] [1 -4 0 1] ) × [1 -4 0 1]
y₂ = [7 -7 -6 1] - (7 + 28 - 0 + 1) / (1 + 16 + 0 + 1) × [1 -4 0 1]
y₂ = [7 -7 -6 1] - 36/18 × [1 -4 0 1]
y₂ = [7 -7 -6 1] - 2 × [1 -4 0 1]
y₂ = [7 -7 -6 1] - [2 8 0 2]
y₂ = [5 1 -6 -1]
That is,
The orthogonal basis for w using Gram-Schmidt process is,
y₁ = [1 -4 0 1] and y₂ = [5 1 -6 -1]
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A carpenter used 29 ft of molding in three pieces to trim a garage door. If the
long piece was 1 ft longer than twice the length of each shorter piece, then
how long was each piece?
Answer:
Let's call the length of the long piece x, and the length of each shorter piece y. We can set up the following equation to represent the problem:
x + 2y = 29
Since the long piece is 1 ft longer than twice the length of each shorter piece, we can write this equation as:
x = 2y + 1
Substituting this expression for x in the first equation, we get:
2y + 1 + 2y = 29
Combining like terms on both sides, we get:
4y + 1 = 29
Subtracting 1 from both sides, we get:
4y = 28
Dividing both sides by 4, we get:
y = 7
Substituting this value for y in the expression for x, we get:
x = 2(7) + 1 = 14 + 1 = 15
Thus, the length of the long piece is 15 ft, and the length of each shorter piece is 7 ft.
10. Why are median and IQR better statistics than mean and standard deviation for describing
skewed probability distributions?
Median and IQR are better statistics than mean and standard deviation for describing skewed probability distributions because it's based on values that come from the middle half of the distribution, it's unlikely to be influenced by outliers.
Why is the IQR and median better?Because it is unaffected by outliers, the IQR is frequently regarded as a more accurate measure of spread than the range. The variance and standard deviation are indicators of how widely the data are dispersed from the mean. Each observed data value's proximity to the mean is summarized.
The best indicator of variability in data sets with outliers or skewed distributions is the interquartile range. It's unlikely to be impacted by outliers because it's based on values that come from the middle half of the distribution.
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a farmer wishes to enclose a rectangular area of 80,000 square feet and divide it into three pens with fencing parallel to one of the sides of the rectangle. what is the minimum amount of fence that he can use?
The minimum amount of fence that he can use is 1600 ft.
Given ;
Area of rectangular = 80,000 sq. ft
i.e. xy = 80,000
Total fencing needed ,
x + y + x + y + 2y = 2x + 4y
To minimize 2x + 4y, constrained to xy = 80,000
i.e. xy = 80,000
⇒ y = 80,000/x
⇒ so, s = 2x + 4 (80,000/x) to be minimized
⇒ To minimum value at ds/dx = 0
i.e. s = 2x + 4 (80,000/x)
= 2x + (3,20,00/x)
⇒ Now, ds/dx = 0 = 2 + (3,20,000) - [tex]\frac{1}{x^{2} }[/tex]
⇒ [tex]\frac{320000}{x^{2} } = 2[/tex]
⇒ [tex]x^{2} = 160000[/tex]
⇒ x = 400
∴ x = 400 ft
y = 80,000/400 = 200
∴ y = 200 ft
Total frencing is
⇒ 2x + 4y = 2 × 400 + 4 × 200
= 800 + 800
= 1600 ft
∴ The minimum amount of fence that he can use is 1600 ft.
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function F is defined by the equation f(x)=x to the power of 2. what is f(2)
The value of f(2) is 4.
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
The domain and range of the function are the set of values of f(x) that are produced by the values in the domain of the function, which is the set of values of x. In addition to f(x), alternative shorthand symbols for functions of the independent variable x include g(x) and P(x), especially when the nature of the function is ambiguous or uncertain.
Given function is
f(x) = x²
Putting x = 2 in the given function:
f(2) = 2²
Putting 2² = 4 in the above function:
f(2) = 4
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find the dimensions of the rectangular corral split into 2 pens of the same size producing the greatest possible enclosed area given 300 feet of fencing.
The dimensions of the rectangular corral:
length = 75 ft and width = 5 ft
Let m be the length of the rectangular corral and n be the width of the rectangular corral.
The perimeter of the rectangular corral,
P = 2m + 2n
The rectangular corral split into 2 pens of the same size.
So, P = 2m + 3n
The 2 pens producing the greatest possible enclosed area given 300 feet of fencing.
300 = 2m + 3n
n = (300 - 2m)/3
Area of the rectangular corral,
A = m * n
A(n) = m * (300 - 2m)/3
A(m) = (300/3)*m - (2/3)*m
Taking derivatives on both sides of the equation:
A'(m) = 100 - (4/3)*m
for A'(m) = 0,
100 - (4/3)*m = 0
m = 100 * (3/4)
m = 75
So, n = (300 - 2(75))/3
n = 50
Therefore, the length of the rectangular corral = 75 ft and width = 5 ft
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3. The Alvarez family bought a car for $2,000. They made a down
payment of $500. If they want to pay the balance in 5 equal
payments, how much will each of these payments be?
The first step is to subtract $500 from $2000 and then you end up with $1500 which you then divide by 5.
Each payment will have to be $300
(1 point) standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed by 2 numbers. how many different standard plates are possible in this system? (assume repetition of letters and numbers is allowed.) your answer is :
Therefore ,there are 158,184,000 ways to create a license plate in this system.
What is combination ?A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations.
According to the counting principle, the total number of ways to obtain a license plate is calculated by multiplying the number of times each of these events might occur together.
The first number (the digits 1 through 9) can be obtained in nine different ways.
There are 26 methods to obtain the first letter. There are 26 ways to obtain the following letter (repetition is acceptable).
There are 26 methods to get the third letter, 10 ways to get the next number (zero is acceptable), and 10 ways to get the following number with repetitions.
How many ways are there to get the next number? 10 ways\s.
Thus ,total options for obtaining a license plate:
9 x 26 x 26 x 26 x 10 x 10=158184000
Therefore ,there are 158,184,000 ways to create a license plate in this system.
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25% of what number is 6?
Answer:it is 24 ∪w∪
Step-by-step explanation: 100% is 24
a newsletter publisher believes that over 62% of their readers own a rolls royce. for marketing purposes, a potential advertiser wants to confirm this claim. after performing a test at the 0.02 level of significance, the advertiser decides to reject the null hypothesis. what is the conclusion regarding the publisher's claim?\
There is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.
Given that,
Over 62% of a newsletter publisher's subscribers, in their estimation, own a Rolls-Royce. A potential advertiser wants to verify this claim for marketing purposes. The advertiser decides to reject the null hypothesis following a test with a significance threshold of 0.02 after executing the analysis.
We have to find what is the verdict in relation to the publisher's assertion.
We know that,
First we have to write the null hypothesis and alternative hypothesis for the hypothesis test.
H₀:P=0.62
H₁:P>0.62
At 0.02 level of significance, rejecting H₀ then accepting H₁.
That is sufficient evidence that percentage over 62%.
Therefore, there is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.
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a company wants to hire a software engineer, an administrative assistant, and a sales representative. there are 4 possible candidates for the position of software engineer, 4 for the position of administrative assistant, and 6 for the position of sales representative. how many ways are there to choose the three people who will be hired?
The number of ways in which we can select a software engineer, an administrative assistant, and a sales representative is 48.
Since we are only choosing one option from each category, the number of alternatives for each category is equal to the number of combinations for each category .
Using the equation for each pair and then adding them up,
C (n,r) = n! / (r! (n - r)! )
we get the required number of combinations as 48.
Factorial
There are n! techniques of arranging n unique things into an ordered sequence, permutations where n = r.
Combination
The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
Permutation
The number of ways to choose a sample of r elements from a set of n distinct objects when order does matter and replacements are not allowed. When n = r this reduces to n! , a simple factorial of n.
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The expression 2r + 3r represents the daily profit, in dollars, earned by an ice cream shop, where r represents the number of batches each type of ice cream sold. The term 2r shows the profit earned through selling vanilla ice cream batches. The term 3r shows the profit earned through selling strawberry ice cream batches. Which equivalent expression can be used to calculate the total daily profit
Answer:
5x
Step-by-step explanation:
when 2 terms have a the same variable you can just add the coeefiects
2x+3x
2+3=5 so 2x+3x=5x
hopes this helps please mark brainliest
use the divergence theorem to evaluate s (5x 7y z2) ds where s is the sphere x2 y2 z2 = 1.
The divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.
What is meant by divergence theorem?Let S be the boundary surface of E with the positive (outward) orientation, and let E be a straightforward solid region. Let F be a vector field with continuous partial derivatives on an open region containing E for each of its component functions. Then
[tex]$\iint_S F \cdot d S=\iint_S F \cdot n d S=\iiint_E div Fdv$[/tex],
where n be the outward normal of S.
Let the given equation be
The sphere S is x² + y² + z² = 1
By using concept,
[tex]$$\iint_S F \cdot n d S=\iint_S\left(2 x+2 y+z^2\right) d S$$[/tex]
Therefore,
[tex]$$F \cdot n=2 x+2 y+z^2$$[/tex]
Given that the sphere S is x² + y² + z² = 1
For S, n will be
[tex]$n=\frac{x i+y j+z k}{\sqrt{x^2+y^2+z^2}}$$[/tex]
After substituting the value of x² + y² + z² = 1
n = x i + y j + z k
Therefore,
F(xi + yj + zk) = 2x + 2y + z²
Consider F = Pi + Qj + Rk
[tex]$& (P i+Q j+R k) \cdot(x i+y j+z k)=2 x+2 y+z^2 \\[/tex]
Px + Qy + Rz = 2x + 2y + z²
By comparing the values, P = 2, Q = 2, R = z
So, F becomes
F = 2i + 2j + zk
By using the definition of Divergence,
[tex]${div} F=\left(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z}\right) \cdot(2 i+2 j+z k) \\[/tex]
[tex]$& =\frac{\partial}{\partial x}(2 i+2 j+z k)+\frac{\partial}{\partial y}(2 i+2 j+z k)+\frac{\partial}{\partial z}(2 i+2 j+z k) \\[/tex]
= 0 + 0 + 1
div F = 1
By using Divergence Theorem,
[tex]$ \iint_S F \cdot n d S=\iiint_E {div} F d V \\[/tex]
[tex]$& \iint_S\left(2 x+2 y+z^2\right) d S=\iiint_E 1 d V[/tex]
Since [tex]$\iiint_E 1 d V$[/tex] is the volume of sphere with radius 1
[tex]$& \iint_S\left(2 x+2 y+z^2\right) d S=\text { Volume of } E \\[/tex]
[tex]$& =\frac{4}{3} \pi(1)^3=\frac{4}{3} \pi[/tex]
Thus,
[tex]$\iint_S\left(2 x+2 y+z^2\right) d S=\frac{4}{3} \pi$$[/tex]
Therefore, the divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.
The complete question is:
Use the Divergence Theorem to evaluate S(2x+2y+z2)dS where S is the sphere x2+y2+z2=1.
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The divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.
What is meant by divergence theorem?
Let S be the boundary surface of E with the positive (outward) orientation, and let E be a straightforward solid region. Let F be a vector field with continuous partial derivatives on an open region containing E for each of its component functions. Then
[tex]\iint_S F \cdot d S=\iint_S F \cdot n d S=\iiint_E d i v F d v[/tex]
where n be the outward normal of S.
Let the given equation be
The sphere S is x² + y² + z² = 1
By using concept,
[tex]\iint_S F \cdot n d S=\iint_S\left(2 x+2 y+z^2\right) d S[/tex]
Therefore,
[tex]\mathrm{F} \cdot n=2 x+2 y+z^2[/tex]
Given that the sphere S is x² + y² + z² = 1
For S, n will be
[tex]n=\frac{x i+y j+z k}{\sqrt{x^2+y^2+z^2}}[/tex]
After substituting the value of x² + y² + z² = 1
n = x i + y j + z k
Therefore,
F(xi + yj + zk) = 2x + 2y + z²
Consider F = Pi + Qj + Rk
[tex](P i+Q j+R k) \cdot(x i+y j+z k)=2 x+2 y+z^2[/tex]
Px + Qy + Rz = 2x + 2y + z²
By using the definition of Divergence,
= 0 + 0 + 1
div F = 1
By using Divergence Theorem,
[tex]\begin{aligned}& \iint_S F \cdot n d S=\iiint_E d i v F d V \\& \iint_S\left(2 x+2 y+z^2\right) d S=\iiint_E 1 d V\end{aligned}[/tex]
Since[tex]\iiint_E 1 d V[/tex]is the volume of sphere with radius 1[tex]$$\begin{aligned}& \iint_S\left(2 x+2 y+z^2\right) d S=\text { Volume of } E \\& =\frac{4}{3} \pi(1)^3=\frac{4}{3} \pi\end{aligned}$$Thus,\iint_S\left(2 x+2 y+z^2\right) d S=\frac{4}{3} \pi[/tex]
Therefore, the divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.
Use the Divergence Theorem to evaluate S(2x+2y+z2)dS where S is the sphere x2+y2+z2=1.
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Work out
(
8.8
×
10
−
2
)
+
(
3.4
×
10
−
4
)
Give your answer in standard form
Answer:
9.14
Step-by-step explanation:
To add these numbers, we first need to rewrite them in standard form, which means expressing them as a number between 1 and 10, multiplied by a power of 10.
The first number, (8.8 × 10^-2), is already in standard form.
The second number, (3.4 × 10^-4), is not in standard form. To rewrite it in standard form, we divide 3.4 by 10 twice:
(3.4 × 10^-4) = (0.34 × 10^-2) = (3.4 × 10^-3)
Now that both numbers are in standard form, we can add them:
(8.8 × 10^-2) + (3.4 × 10^-3) = 8.8 + 0.34 = 9.14
The final answer is 9.14.
Answer:
9.14
(8.8 × 10 − 2) + (3.4 × 10 − 4) = 9.14
the cdc estimated that 12% of women who have recently given birth suffer from ppd. however, this research only reflected self-reported cases. therefore, one group dedicated to helping women and their families with ppd believes that the true percentage of women who suffer from ppd is much higher. the group conducts a simple random sample of 139 women who had given birth in the last year and discovers that 25 of them report having ppd. based on this evidence, can the group claim that the true percentage of women who have ppd is greater than 12%? use a 0.05 level of significance. step 2 of 3 : compute the value of the test statistic. round your answer to two decimal places.
The actual percentage of female people with ppd is more than 12%.
What is ppd ?Many women experience postpartum depression (commonly known as PPD), which is a medical disorder. After giving delivery, there are intense emotions of sadness, anxiety (concern), and exhaustion that persist for a long time. You may find it challenging to care for both you and your infant as a result of these feelings. PPD can occur at any point following childbirth. Within 1 to 3 weeks of giving birth, it frequently begins. To get better, it need treatment.
What does true percentage mean in statistics?And that's basically what TS% is. A measure of scoring efficiency based on the number of points scored over the number of possessions in which they attempted to score. The actual TS% formula multiplies the denominator by 2 to put the number into a percentage scale, but it's the same result on a different scale
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How do you solve 13=8−5d?
By solving 13 = 8- 5d we get the value of ‘d ’ is equal to -1.
This equation can be solved by arranging the non – algebraic equations on one side and letting the algebraic number on the other side.
13 = 8 – 5d
5d = 8-13
5d = -5
d = -5/5
d = -1.
While arranging the non - algebraic numbers on one side their signs should be changed after taking the number into another side. Similarly, while arranging the algebraic equations on one side, signs of the numbers should be changed. In an algebraic equation, the terms addition, subtraction, multiplication, division, raising to a power, and extraction of a root are applied to a set of variables to construct a statement of the equality of two expressions.
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Gary's cat weighs 11 pounds. How many ounces does Gary's cat weigh?
Answer:
Gary would weigh 176 ounces.
Step-by-step explanation:
One pound is sixteen ounces so just multiply sixteen and 11. ( 16 * 11 = 176 )
I hope this helped you! Have an amazing day :)
Answer: 176 ounces
Step-by-step explanation:
To convert pounds to ounces, multiply the initial value by 16. Since we have the weight of Gary's cat as 11 pounds, their weight in ounces should be 11 * 16 = 176 ounces.
if you have 10 apples and eat 7 halves how much apple do u have left?
You will have 3 1/2 left of apples
Answer:6.5 apples
Step-by-step explanation:
7 *.5=3.5 whole apples
10 apples- 3.5 apples=6.5 apples
(1 point) how many strings of 4 lower case english letters are there that have the letter x in them somewhere? here strings may use the same letter more than once. (hint: it might be easier to first count the strings that don't have an x in them.) your answer is:
Therefore, number of strings can be made by using 4 lower case english letters is 66,351 strings.
What is combination?Combination refers to an arrangement of objects where the order is not crucial. Contrary to permutation, where the order is important. Consider how the letters A, B, and C would be arranged. ABC and ACB are not the same arrangement in a permutation.
Here,
Repetition is permitted as long as we're only looking at lowercase letters.
Number of strings of length 4=[tex]26^{4}[/tex]
Other than x, how many strings of length 4 exist=[tex]25^{4}[/tex]
[tex]26^{4}[/tex]- [tex]25^{4}[/tex]=66,351 strings.
Therefore number of strings can be made by using 4 lower case english letters is 66,351 strings.
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the president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean sat score is lower than previous years. he took a sample of 30 of this year's entering students and found that their mean sat score is 1,501 with a standard deviation of 53. the university's record indicates that the mean sat score for entering students from previous years is $1,520. he wants to find out if his claim is supported by the evidence at a 5% significance level. which of the following best describes a type i error? the president concludes that the mean sat score of the entering students is lower than previous years when it is indeed not lower the president concludes that the mean sat score of the entering students is higher than previous years when it is indeed higher the president concludes that the mean sat score of the entering students is not lower than previous years when it is indeed lower the president concludes that the mean sat score of the entering students is lower than previous years when it is indeed lower
The result is not statistically significant.
To test the hypothesis is the mean SAT score is less than 1520 at 5% significance level.
The null hypothesis is
H₀ : μ ≥ 1520
The alternative hypothesis is
Hₐ : μ ≤ 1520
then the test statistic is,
t = (x - μ)/(s/√n)
= (1501 - 1520)/(53/√20)
t = - 1.603
The t-test statistic is - 1.603.
Degree of freedom n - 1 = 20 - 1 = 19
Hence the t-critical value is -1.792.
The conclusion is that the t value corresponds to sample statistics is not fall in the critical region, so the null hypothesis is not rejected at 5% level of significance. There is insignificance evidence indicates that the mean SAT score is less than 1520.
The result is not statistically significant.
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If Monica has 60 arces of land and each goat required 1/3 of an acre, how many goats can her land support?
A. 100
B. 180
C. 300
D. 120
Answer: B.180
Step-by-step explanation:
number of acres = 60
area required for one goat = 1/3 of an acre
number of goats one acre can hold = 3
number of goats her land can support = 60*3 = 180
Find The Value Of X.
Answer:
Step-by-step explanation:
x+80=145
x=65
A recipe for one batch of cookies calls for 3 cups of sugar and 2 tablespoons of salt.
How many batches can you make with 12 cups of sugar and 8 tablespoons of salt?
what's the answer 7x + 7=7(x+_)
the answer is 1
Step-by-step explanation:
there are 6 students in the class. one of them is to be selected as the best student and another student is to be selected as a runner-up. how many different ways can this be done?
If there are 6 students and one is selected for best student and another is selected for runner up, then 15 different ways that we can arrange the students
Total number of students in the class = 6 students
Number of students for best student = 1 student
Number of students for runner up = 1 students
Total number of students needed = 2
Here we have to use the combination
6[tex]C_2[/tex] = 6! / 2!(6 - 2)!
= 6! / 2! × 4!
Split the terms and cancel it
= 6 × 5 / 2 × 1
Multiply the terms
= 30 / 2
Divide the numbers
= 15 combinations
Therefore, there are 15 combinations
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Which one would it be?
Solving the given equation we get value of x as -3/2 i.e option (a) is correct option.
What are exponents and its properties?
A number's exponent indicates how many times the number has been multiplied by itself. Example: Since 2 is multiplied by itself 4 times, 2×2×2×2 can be expressed as [tex]2^{4}[/tex]. Here, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base."
Generally speaking, [tex]x^{n}[/tex] denotes that x has been multiplied by itself n times.
Raise a power to a power
[tex](x^{a}) ^{b}=x^{ab}[/tex]
This is called the power of a power property
Negative exponents are the reciprocals of the positive exponents.
[tex]x^{-a}=\frac{1}{x^a}[/tex]
The same properties of exponents apply for both positive and negative exponents.
[tex](1/25)^x = 125\\ 25^{-x} = 125\\(5^2)^{-x} = 5^3\\5^{-2x} = 5^3\\\implies -2x = 3\\\implies x = -3/2[/tex]
i.e.
Option (a) is correct.
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