5) The hypotenuse of a right
triangle is 45 inches, with one of
the legs being 18 inches. Find the
missing side length. Round to the
nearest tenths if necessary.

Since -1.7 > -2.33, we faiI tο reject the nuII hypοthesis. Therefοre, we cannοt cIaim with 99% cοnfidence that the mean weight οf the manufacturer's cοmputer parts is Iess than 275 grams

Standard deviatiοn is a statisticaI measure that shοws hοw much variatiοn οr dispersiοn there is frοm the mean οf a set οf data. It is caIcuIated by finding the square rοοt οf the variance.

Tο test this hypοthesis, we need tο perfοrm a οne-sampIe t-test with the fοIIοwing hypοtheses:

NuII hypοthesis: The mean weight οf the cοmputer parts prοduced by the manufacturer is greater than οr equaI tο 275 grams.

AIternative hypοthesis: The mean weight οf the cοmputer parts prοduced by the manufacturer is Iess than 275 grams.

We wiII use a οne-taiIed test with a IeveI οf significance οf 1%, which cοrrespοnds tο a t-scοre οf -2.33 (frοm the t-distributiοn tabIe with 255 degrees οf freedοm).

The test statistic fοr this sampIe is:

t = (sampIe mean - hypοthesized mean) / (sampIe standard deviatiοn / √(sampIe size))

t = (274.3 - 275) / (25.9 / √(256))

t = -1.7

Since -1.7 > -2.33, we faiI tο reject the nuII hypοthesis. Therefοre, we cannοt cIaim with 99% cοnfidence that the mean weight οf the manufacturer's cοmputer parts is Iess than 275 grams

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Answer:Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.

Step-by-step explanation:The mean weight from a sample of 256 computer parts created by a computer manufacturer was 274.3 grams, with a standard deviation of 25.9 grams. Can this company claim that the mean weight of its manufactured computer parts will be less than 275 grams? Test this hypothesis using a 1% level of significance.

Reject the null hypothesis. There is not enough evidence to oppose the company's claim.

Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.

Reject the null hypothesis. There is enough evidence to oppose the company's claim.

Fail to reject the null hypothesis. There is enough evidence to oppose the company's claim.

The test statistic needs to fall within the rejection regions that are above and below the critical z-score associated with a 1% level of significance in order to reject the null hypothesis. Otherwise, we will fail to reject the null hypothesis.

1

Points

/ 1

The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1

To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.

Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.

Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.

On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.

Option 1 is correct.

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Answer:

8/19

Step-by-step explanation:

The probability that a student is chosen randomly from the class passed the test and completed the homework will be 0.1637.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

In a math class with 19 students, a test was given the same day that an assignment was due.

There were 10 students who passed the test and 11 students who completed the assignment.

There were 6 students who failed the test and also did not complete the assignment.

Then the probability that a student is chosen randomly from the class passed the test and completed the homework will be

The number of the student who has done at least one assignment or passed the test is 19 - 6 = 13

n(A) = passes student

n(B) = given assignment

Then we have

\(\rm n(A \cap B) = n(A) + n(B) - n(A \cup B) \\\\n(A \cap B) = 10 + 11 - 13\\\\n(A \cap B) = 8\)

Then the probability will be

\(\rm P = \dfrac{^8C_2}{^{19}C_2}\\\\P = \dfrac{28}{171}\\\\P = 0.1637\)

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Answer:

42

Step-by-step explanation:

let's make the missing number x

\(mean = \frac{sum \: of \: numbers}{how \: many \: numbers \: there \: are} \)

\(41 = \frac{48 + 33 + x}{3} \)

multiply 3 on both sides to get rid of the fraction, 41 × 3 = 123

\(123 = 48 + 33 + x\)

simplify the right side, 48 + 33 = 81

\(123 = 81 + x\)

subtract 81 on both sides

\(123 - 81 = x\)

\(x = 42\)

Answer:

Step-by-step explanationuuh soo I don’t understand this app:

The probability of getting at least two heads is 0.965

Given that

Number of times fair coin tossed = 8

Since we know

The probability of getting head  in single toss = 1/2

And  probability of getting tail  in single toss = 1/2

Now, there are 247 combinations to get least two heads (256—1–8=247).

Therefore,

The probability of getting at least two heads

=  247/256 or 0.965…

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The equation of the line perpendicular to 7x+5y = 4 is y = 5/7(x) -15/7. The equation of the line parallel to 7x+5y = 4 is  y = -7/5(x) -53/5

Given that: the line is perpendicular/parallel to the line 7x+5y = 4 and it passes through (−4,-5)

The slope-intercept form of a straight line is:

y = mx + c

where m is the slope and c is the y-intercept

For perpendicular case:

When the two lines are perpendicular, the product of their slope is -1 i.e.

m₁ x m₂ = -1

where m₁ and m₂ represent the slope of the lines

Let the slope of the given line be m₁ and the slope of the unknown line be m₂

Line1(given):

7x+5y = 4  => y = (-7/5)x + 4/5

Thus,  m₁ = -7/5

m₁ x m₂ = -1

-7/5 x m₂ = -1

m₂= 5/7

Line 2(unknown) with the point (−4,-5):

y = mx + c

-5 = 5/7 (-4) + c

-5 = -20/7 + c

c = -15/7

Thus, the equation of the line is y = 5/7(x) -15/7

For parallel case:

When the two lines are parallel, they have equal slope i.e. m₁ = m₂

Line1(given):

7x+5y = 4  => y = (-7/5)x + 4/5

Thus,  m₁ = -7/5

m₂= -7/5

Line 2(unknown) with the point (−4,-5):

y = mx + c

-5 = -7/5(-4) + c

-5 = 28/5 + c

c = -53/5

Thus, equation of the line is y = -7/5(x) -53/5

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Answer:

9. 2:50 . she left after 40 minutes meaning you have to subtract 3:30 and 40 . so 30 mins is 3:00 and then you take away another 10 to make it 40 minutes ago and you get 2:50 pm

Answer:

36, 525, 795, and 84

Step-by-step explanation:

36/3=12

525/3=175

795/3= 265

84/3=28

Answer:

b

Step-by-step explanation:

Answer:

2.4*18 = $43.2

stock price is $43.2

Step-by-step explanation:

The probability that a person will purchase no more than one costume is given as follows:

93%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes for this problem is given as follows:

187 + 228 + 29 = 444.

Only 29 people purchased more than one costume, hence the probability of at most one costume is calculated as follows:

(444 - 29)/444 = 0.93 = 93%.

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Answer:

1. you have to write down Some nubers in the koordinatsystem

than you can read that it is(if you use only one Box) (-6|5)(6|1)

Answer:

what is the time given ???

Step-by-step explanation:

either initial velocity is 0 or final velocity is zero

V=U+AT

converting it we get

V/T = u+a

V/T - U= a

where

v= final velocity

u= initial velocity

a= acceleration

t= time

plz write the full question

\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Ace Hardware sold 48 boxes of pens and Ace Hardware sold 240 batteries

Cost for batteries = $3

Cost of small boxes of pens = $5

Total sales = $960

let number of batteries = b

number of boxes of pens = p

Cost for batteries (number of batteries) + Cost of small boxes of pens (number of boxes of pens) = Total sales

From the questions, customers bought 5 times as many batteries as boxes of pens

b = 5 times of p

Using substitution method

From equation 2, b ihas been made the subject of formula.

susbtitute for b in equation (1):

substitute for p in equation (2):

Hence, Ace Hardware sold 48 boxes of pens and Ace Hardware sold 240 batteries

Answer:

y = (-3x/5) +1

Step-by-step explanation:

We know that the line passes through the point (-5 , 4)

AND

the slope is given to be -3/5

let's look at the slope a bit more

we know that the formula for slope of a line is Rise / Run

Which means that the rise of this line is -3 after spanning 5 units to the right

Hence, the line goes down 3 units after moving 5 units to the right

We know that to find the equation of a line through the point-slope equation, we need the slope as well as the y-intercept of the line

since we are already given the slope, we need to find the point where the line intersects the y-axis

Now, back to the given point the line passes through

this point has a x - coordinate of -5 and we know that after moving 5 units to the right, the line moves 3 units downwards

So, if the line moves 5 units to the right from the given point, it will reach the y- axis and we know that it's y-coordinate will decrease by 3

Hence, the y-intercept will be 3 units below the given y -coordinate

y - intercept = (4 - 3) =  1 = y-intercept

Now, using the slope-intercept formula to get the equation:

y =  (slope)*x + (y-intercept )

y = (-3/5)x + (1)

y = (-3x/5) + 1

Answer: 5/24

Step-by-step explanation:

(-2/3)+(7/8)=

(-2/3)+(7/8)*24/24=        ==> 24 is the LCM of 3 and 8

\(\frac{(-2*24)/3+(7*24)/8}{24}\)=

\(\frac{-2*24/3+7*24/8}{24}\)=

\(\frac{-2*8+7*3}{24}\)=

\(\frac{-16+21}{24}\)=5/24

Answer:

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

76 words per minute.

Step-by-step explanation:

49 min = 3724 words

1 min = ?

3724/49 = 76

1 min = 76 words

Hope this helps!!

Step-by-step explanation:

yes, the step is correct.

a² = cx | multiply by c

ca² = c²x

I am just not sure how that simplified the equation.

what do you want to achieve ? what's the goal here ?

to solve the equation for x it would be to divide both sides by c, which gives

a²/c = x

Answer:

80%

Step-by-step explanation:

If you divide 52 by 65 you will get a decimal, then multiply by 100% to get the equivalent.

52/65 = 0.8

0.8 x 100 = 80%

Answer:

Step-by-step explanation:

A ratio is a comparison of two quantities, typically written in the form a:b or a/b. For example, a ratio of 2:3 represents a comparison of two quantities where the first quantity is 2 and the second quantity is 3.

The related rate of a ratio is the rate at which the ratio changes over time. For example, if the ratio of the number of apples to the number of oranges in a basket is 2:3, and the number of apples is increasing at a rate of 2 apples per minute, then the related rate of the ratio would be 2:3 per minute.

A unit rate is a special type of rate in which the denominator of the ratio is 1. For example, if the ratio of the number of apples to the number of oranges in a basket is 2:1, then the unit rate is 2 apples per orange. Unit rates are often used to compare quantities that are measured in different units.

Answer:

3:8 or 3 to 8 depending on how you personally write it

Step-by-step explanation:

In problems like these you just need to put the numbers in the order that the question asks you in. In this case it is asking for drink mix (3) to water (8) making it 3:8.

Answer:

I saw another question like this but it was the other way like "water to drink mix" and it was 8:3 so technically and mathematically it would be 3:8

Step-by-step explanation:

The given shape of the distribution is not symmetric.

Given that, a box plot shows donations in dollars to charity.

We need to describe the shape of the distribution.

Donations to Charity ($) =

20 40 60 80 100 120 140 160 180 200 220

so, as we can see,

The shape of the distribution is not symmetric since the lengths of each box and whisker are not the same. There is an outlier at 220.

Hence, the given shape of the distribution is not symmetric.

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Answer: 16875x³-13500x²+3600x-320

Step-by-step explanation:

[gοfοh](x) means g(f(h(x))). So you plug in h(x) into f(x) and that into g(x).

f(3x)=5(3x)-4=15x-4

g(f(3x))=5(15x-4)³

g(f(3x))=5(3375x³-2700x²+720x-64)

g(f(3x))=16875x³-13500x²+3600x-320

Answer:

A

Step-by-step explanation: