Every year, a dog sled race is held in Alaska and is approximately 1,150 miles in distance. Information about the top three racers is
listed below.
• Aaron completed half the race in approximately 4 days, 12 hours.
• Dallas finished the race in approximately 8 days, 18 hours.
• Mitch completed one-quarter of the race in approximately 2 days, 5 hours.

The P-value is between 0.025 and 0.05. and t = -1.85

On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.

Therefore tests the hypotheses:

\(H_0\) : μ = 25 versus Ha: μ < 25,

where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.

The alternative hypothesis is:

\(H_1:\mu < 25\)

The test statistic is given by:

\(t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }\)

The parameters are:

the values of the parameters are:

x = 23.5 , \(\mu=25\) , s = 4.8, n = 35

Plug all the values in above formula of t- statistic is:

\(t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }\)

t = -1.85

Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.

t = –1.85; the P-value is between 0.025 and 0.05.

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Answer:

Step-by-step Solution:

Hence, Option B is correct.

Answer:

1.The  equation of best fit is ŷ = 2.69152X + 3.45818.

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Edge 2021

Answer

i don't understand

step-by-step explanation:

Answer:

21.3

Step-by-step explanation:

Answer:

\(b_1=\left(\begin{array}{ccc}-3\\3\end{array}\right),b_2=\left(\begin{array}{ccc}-\dfrac{65}{11}\\\\-\dfrac{19}{11}\end{array}\right)\)

Step-by-step explanation:

Given matrix A and AB below:

\(A=\left(\begin{array}{ccc}1&-4\\-4&5\end{array}\right)\\\\\\ AB=\left(\begin{array}{ccc}-10&1&9\\7&-15&8\end{array}\right)\)

For the product AB to be a 2 X 3 matrix, B must be a 2 X 3 matrix.

Let matrix B be defined as follows

\(B=\left[\begin{array}{ccc}a&c&e\\b&d&f\end{array}\right]\)

Therefore:

\(\left(\begin{array}{ccc}1&-4\\-4&5\end{array}\right)\left(\begin{array}{ccc}a&c&e\\b&d&f\end{array}\right)=\left(\begin{array}{ccc}-10&1&9\\7&-15&8\end{array}\right)\)

This results in the equations

Solving the first two equations simultaneously

a-4b=-10  (a=-10+4b)

-4a+5b=7

Substitution of \(a=-10+4b\) into the second equation

\(-4(-10+4b)+5b=7\\40-16b+5b=7\\-11b=-33\\b=3\)

Recall that  \(a=-10+4b\)

\(a=-10+4(3)=-10+7\\a=-3\)

Solving the other two equations

c-4d=1 (c=1+4d)

-4c+5d=-15

Substitution of c=1+4d into the second equation

\(-4(1+4d)+5d=-15\\-4-16d+5d=15\\-11d=19\\d=-\dfrac{19}{11}\\ Recall: c=1+4d\\c=1+4(-\frac{19}{11})\\c=-\dfrac{65}{11}\)

Therefore, we have:

\(a=-3, b=3, c=-\dfrac{65}{11}, d=-\dfrac{19}{11}\)

Thus:

\(b_1=\left(\begin{array}{ccc}-3\\3\end{array}\right)\\\\\\b_2=\left(\begin{array}{ccc}-\dfrac{65}{11}\\\\-\dfrac{19}{11}\end{array}\right)\)

Answer:

option c

Step-by-step explanation:

it is said that a computer repairman makes 25 dollars per hour

this column shows the right amount of money he earns per hour

Answer:110 degrees

Step-by-step explanation:

There is no Unique solution for b.to solve for a and b in an algebraic equation, we need to choose a variable to solve for, isolate that variable, solve for it, and then use that equation to solve for the other variable.

To solve for a and b in an algebraic equation, we need to know the values of the other variables in the equation. Here's an example of how to solve for a and b in the equation 2a + 3b = 12:
Step 1: Choose a variable to solve for
In this equation, we can choose to solve for either a or b. For this example, let's solve for a.
Step 2: Isolate the variable
We want to get a by itself on one side of the equation. To do this, we need to move the other terms to the other side of the equation. We can start by subtracting 3b from both sides of the equation:
2a + 3b - 3b = 12 - 3b
Simplifying:
2a = 12 - 3b
Step 3: Solve for the variable
To solve for a, we need to get it by itself on one side of the equation. We can do this by dividing both sides of the equation by 2:
2a/2 = (12 - 3b)/2
Simplifying:
a = 6 - (3/2)b
Step 4: Solve for the other variable
We can use the equation we found for a to solve for b. Substituting a with 6 - (3/2)b in the original equation, we get:
2(6 - (3/2)b) + 3b = 12
Simplifying:
12 - 3b + 3b = 12
Since the 3b terms cancel out, we're left with:
12 = 12
This equation is true no matter what value of b we choose. Therefore, there is no unique solution for b.
In conclusion, to solve for a and b in an algebraic equation, we need to choose a variable to solve for, isolate that variable, solve for it, and then use that equation to solve for the other variable.

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The length of the side opposite to the reference angle is 7.77 units.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle 45°, The side 'x' is opposite and the side having a length of 11 units is the hypotenuse.

We know, sin = opposite/hypotenuse.

Therefore,

sin45° = x/11.

1/√2 = x/11.

x = 11/√2.

x = 7.77 units.

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The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;

1. The area is about 15.16 units²

2. The coordinates of the points are;

(i) B(5, 8)

(ii) C(8.58, 4)

(ii) D(8,58, 1.21)

A quadrilateral is a four sided polygon.

1. The coordinate of the point C can be found as follows;

Let (x, y) represent the coordinates of the C, we get;

(x + 8)/2 = 5

x = 2 × 5 - 8 = 2

(y + 8)/2 = 6

y = 2 × 6 - 8 = 4

The coordinates ot the point C (2, 4)

The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)

Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)

The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13

CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;

(4 - y)/(2 - x) = -(5 - x)/(6 - y)

y - 4 = (-4/7)(x - 2)

y - 6 = (7/4)(x - 5)

(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6

x = (17/5) = 3.4

y = (7/4)((17/5) - 5) + 6 = 3.2

The coordinates of the point E is (3.4, 3.2)

The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)

Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)

Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)

Area of the figure is therefore;

2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))

y - 6 = (1/3)·(x + 1)

y = (1/3)·(x + 1) + 6

The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2

Slope of the segment BE = -1/(-1/2) = 2

Equation of BE is; y - 4 = 2·(x - 3)

y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6

Therefore, x = 5

y = (1/3)·(5 + 1) + 6 = 8

(ii) Area of the triangle EBC = 24 unit²

EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20

Therefore;

BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)

(x - 5)² + (y - 8)² = 28.8

y = 4, therefore;

(x - 5)² + (4 - 8)² = 28.8

(x - 5)² = 28.8 - (4 - 8)² = 12.8

x = √(12.8) + 5

(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)

x = √(12.8) + 5

Therefore;

y - 4 = (-1/2)((√(12.8) + 5) - 3)

y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21

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The tax revenue generated from property taxes is often used to fund expressions public services such as schools, parks, and infrastructure projects in the local community.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the expression 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +. The calculation of property tax is typically based on the assessed value of the property and the tax rate set by the local government. The assessed value is determined by a government-appointed assessor who evaluates the value of the property based on factors such as its location, size, age, and condition. The tax rate is then applied to the assessed value to determine the amount of tax owed by the property owner. The tax revenue generated from property taxes is often used to fund public services such as schools, parks, and infrastructure projects in the local community.

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Answer:

4) d. 30%. 5) 55/21. 6) 16

Step-by-step explanation:

4) 6/20 × 100 = 30%

5) Change mixed numbers to fraction. So you're getting 58/7 - 17/3. LCM = 21

= 174 - 119 / 21

= 55 / 21

6) Change to fraction

8/3 ÷ 1/6

= 8/3 × 6/1

= 16

Hello!

\(\large\boxed{(4, -150)}\)

We can solve for the vertex by completing the square. Begin by factoring out 6 from the equation to simplify the process:

6(x² - 8x) - 54 = 0

To complete the square, we must look at the first two terms (x² - 8x).

Remember that squaring a binomial uses the format a² + 2ab + b². We are already given a² and 2ab², so solve for b:

-8 / 2 = -4. This is the value of b.

We can rewrite this as:

(x - 4)²

However, this produces +16 which much be taken into account. Substitute (x - 4)² into the original equation:

6(x - 4)² - 54 = 0

Multiply 16 by the term in the front and subtract to cancel out this term:

6(x - 4)² - 54 - (6 · 16) = 0

Simplify:

6(x - 4)² - 150 = 0

In this form, the vertex is given as:

a(x - h)² + k, where h = x-coordinate and k = y-coordinate of the vertex.

In this instance, h = 4 and k = -150, so the coordinates of the vertex are:

(4, -150)

Answer:

y = 6x²-48x-54 has a vertex at (4,-150)

Step-by-step explanation:

There is no vertex. The solution set to 6x²-48x-54 = 0 is two points, (-1,0) and (9,0).

If you mean y = 6x²-48x-54, that is an up-opening parabola.

Put the equation into vertex form:

y = 6x²-48x-54

 = 6(x²-8x)-54

 = 6(x²-8x+4²)-6·4²-54

 = 6(x-4)² - 150

vertex at (4,-150)

Answer:

36.37%

Step-by-step explanation:

30 - 22 = 8

100% * 8/22

800/22

36.37%

Answer:

statement : ABCD is a parellogram reason: given

To solve this question, the real rate of return formula is used, and we apply the data given in the exercise into the formula to find the real rate of return.

Formula for the real rate of return:

\(R = \frac{1 + N}{1 + i} - 1\)

In which N is the nomial rate and i is the inflation rate, as decimals.

A certificate of deposit offers a nominal interest rate of 2.5 percent annually.

This means that \(N = 0.025\)

Inflation is 1 percent

This means that \(i = 0.01\)

What is the real rate of return:

Now we apply the formula:

\(R = \frac{1 + 0.025}{1 + 0.01} - 1\)

\(R = 1.0149 - 1\)

\(R = 0.0149\)

0.0149*100% = 1.49%

Thus, the real rate of return is of 1.49%.

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Step-by-step explanation:

first you need to tranfer 1 to RHS do the addition

n/3 = 8+1

=) n/3 = 9

then you need to transfer 3 to RHS and multiply

=> n = 9 x 3

there for n = 27

$480 is the maximun

480 ≥ New bicycle + bicycle reflectors + Pair of bike gloves + outfits* o

o = number of outfits

_______________

New bicycle $427.79

bicycle reflectors 2* $10.31= 20.62

Pair of bike gloves 29. 94

________________________

480 ≥ New bicycle + bicycle reflectors + Pair of bike gloves + outfits* o

480 ≥ 427.79 + 20.62 + 29. 94 + 47.45 * o

480 ≥ 478.35 + 47.45 * o

478.35 + 47.45 * o ≤ 480

the first choice

Answer:

(- 3, 1.5)

--------------------------

Given system:

The first expression is ready to be substituted as no further operation is required to simplify it.

Find x:

Answer:

option a i got ti right on the test

Step-by-step explanation:

An equivalent form of the compound inequality −33 > −3x − 6 ≥ −36 will be −3x − 6 < −33 and −3x − 6 ≥ −36. The correct option is B.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

Given that the compound inequality is −33 > −3x − 6 ≥ −36.

In the given inequality the expression -3x - 6 is greater than the value -36 and less than the value -33. Then the split form of the inequality will be written as below:-

−3x − 6 < −33

−3x − 6 ≥ −36

Therefore, an equivalent form of the compound inequality −33 > −3x − 6 ≥ −36 will be −3x − 6 < −33 and −3x − 6 ≥ −36. The correct option is B.

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Answer:

$63.75

Step-by-step explanation:

Stereo costs : $75

Decreased Price :- ( $75 * 15% = 11.25   ,    75 - 11.25 = 63.75 )

So the price after the discount is $63.75.

Answer:

3/6^2

Step-by-step explanation:

First option

\(\huge\bold{Given :}\)

Angle a = 39°

Angle c = 123°

\(\huge\bold{To\:find :}\)

The measure of angle b.

\(\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}\)

∠ b = 18°

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

We know that,

\(\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}\)

➪ ∠ a + ∠ b + ∠ c = 180°

➪ 39° + ∠ b + 123° = 180°

➪ ∠ b + 162° = 180°

➪ ∠ b = 180° - 162°

➪ ∠ b = 18°

Therefore, the measure of ∠ b is 18°.

\(\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}\)

∠ a + ∠ b + ∠ c = 180°

✒ 39° + 18° + 123° = 180°

✒ 180° = 180°

✒ L. H. S. = R. H. S.

\(\boxed{Hence\:verified.}\)

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}\)

\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

Step-by-step explanation:

the radius is diameter divided by 2

7/2/2 =1 .75

circumference of a circle is 2πr

2*22/7*1.75=11

3.14*11 =34.54

Answer:

15 apples

Step-by-step explanation:

It's kinda obvious ;-;

Answer: 15 because it + so 5 + 10 = 15

Step-by-step explanation:

Answer:

0.5319 = 53.19% probability that the young man is taller than the young woman by more than 5 inches

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Distribution of the difference in height between men and woman:

Applying the concept above:

\(\mu = 69.3 - 64 = 5.3\)

\(\sigma = \sqrt{2.7^2 + 2.8^2} = 3.89\)

What is the probability that the young man is taller than the young woman by more than 5 inches?

Probability of the difference being more than 5 inches, that is, 1 subtracted by the pvalue of Z when X = 5.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{5 - 5.3}{3.89}\)

\(Z = -0.08\)

\(Z = -0.08\) has a pvalue of 0.4681

1 - 0.4681 = 0.5319

0.5319 = 53.19% probability that the young man is taller than the young woman by more than 5 inches

Step-by-step explanation:

Pressure = Force / Area

= 64N / 3.2m² = 20Pa. (2s.f.)

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The gcf is 12, so you'll divide 12 to both the 48 and the 180.

So it'll look like this...

\(12(4e+15)\)

P.S. don't forget to the "e"

If you want to check if you're right just distribute the 12 and you should get 48e + 180 if you didn't you did something wrong.