answer this question​

[tex]\textit{Law of Cosines}\\\\ \cfrac{a^2+b^2-c^2}{2ab}=\cos(C)\implies \cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C \\\\[-0.35em] ~\dotfill\\\\ \cos^{-1}\left(\cfrac{4^2+7^2-9^2}{2(4)(7)}\right)=\measuredangle C \implies \cos^{-1}\left(\cfrac{ -16 }{ 56}\right)=\measuredangle C \\\\\\ \cos^{-1}\left(\cfrac{ -2 }{ 7}\right)=\measuredangle C\implies \boxed{106.60^o\approx \measuredangle C}[/tex]

Answer:

B) 75

Step-by-step explanation:

Plot the points on the graph and go up to where it matches the other points a little bit. (if that makes sense lol) If you want me to explain it better just let me know lol.

Since line segment MN is congruent to line segment PQ, the value of x is equal to 7.

In Mathematics and Geometry, the chord of a circle can be defined as a line segment that typically join any two (2) points on a circle. This ultimately implies that, a chord simply refers to the section of the line that is used for connecting two (2) separate points on a circle.

In this context, we can reasonably infer and logically deduce that line segment MN is congruent to line segment PQ;

7x + 13 = 10x - 8

10x - 7x = 13 + 8

3x = 21

x = 21/3

x = 7.

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It will take the baseball is 0.64 seconds to hit the ground

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

Initial height = 4 feet

Initial velocity = 4 feet per seconds

So, the function is given as

h = −16t^2 + 4t + 4

When it hits the ground, we have

h = 0

So, we have

−16t^2 + 4t + 4 = 0

Divide through by 4

So, we have

-4t^2 + t + 1 = 0

Using a graphing tool, we have

t = 0.64

Hence, the time is 0.64 seconds

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Using the compound interest formula, the time it takes the investment to double is 0.68 years

To find the time it takes the investment to double, we use the compound interest formula.

A = P(1 + r)ⁿ where

So, making n subject of the formula, we have that

n = ㏑(A/P)/(1 + r)

Since we want to find the time it takes the investment to double, we have that

So, substituting the values of the variables into the equation, we have that

n = ㏑(A/P)/(1 + r)

n = ㏑(2P/P)/(1 + 0.0133)

n = ㏑(2)/(1.0133)

n = 0.693/1.0133

n = 0.68 years

So, the time is 0.68 years

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If the cylindrical-barrel has volume of 785.4 ft³, then the radius of the barrel is 5 ft, option(c) is correct.

We know that volume of cylindrical barrel is given by formula : V = πr²h

where V denotes volume, r denotes radius, and h denotes height of the cylinder.

In this case, we are given that the volume of the barrel is 785.4 ft³ and the height is 10 ft.

Substituting these values and taking π ≈ 3.14, into the Volume-formula,

We get,

785.4 = 3.14 × r² × (10);

Simplifying this equation,

We get,

785.4/31.4 = r²,

r = √(785.4/31.4),

r ≈ 5 ft

Therefore, the radius of the barrel is approximately 5 feet, correct option is (c).

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Answer:

21) 130

22) 146

23) 113

24) 150

Step-by-step explanation:

21)

m<BAC = 50

m<BAO = m<CAO = (1/2)m<BAC = (1/2)(50) = 25

A radius intersects a tangent at a right angle, so m<B = 90.

m<BAO + m<B + m<AOB = 180

25 + 90 + m<AOB = 180

m<AOB = 65

m<BOC = 2 × m<AOB = 2 × 65 = 130

22)

m<BAC = 34

m<BAO = m<CAO = (1/2)m<BAC = (1/2)(34) = 17

A radius intersects a tangent at a right angle, so m<B = 90.

m<BAO + m<B + m<AOB = 180

17 + 90 + m<AOB = 180

m<AOB = 73

m<BOC = 2 × m<AOB = 2 × 73 = 146

23)

m<AOB = (1/2)m<BOC = (1/2) × 67 = 33.5

m<BAO + m<B + m<AOB = 180

m<BAO + 90 + 33.5 = 180

m<BAO = 56.5

m<BAC = 2 × m<BAO = 2 × 56.5 = 113

24)

m<AOB = (1/2)m<BOC = (1/2) × 30 = 15

m<BAO + m<B + m<AOB = 180

m<BAO + 90 + 15 = 180

m<BAO = 75

m<BAC = 2 × m<BAO = 2 × 75 = 150

Where the above data and or function are given, note that the missing value in the table is 7.768

The table is reconstructed as follows:

x        y

4        6.4

4.3     6.88

4.8       ?

5.2       8.32

Thus, merely taking a look at the values of x, a pattern is established.

We can see that x is increasing by 0.5.

To derive the missing value of y given x, we have to

1) compute the difference int he values of y for each respective x

we can say

y(5.2) - y(4.3) = 8.32 - 6.88 = 1.44

To find the value of y for x = 4.8:

y(4.8) = y(4.3) + (0.5/0.9) * (y(5.2) - y(4.3))

⇒ y(4.8) = 6.88 + (0.5/0.9) * 1.44

y (4.8) = 7.68

Hence, the missing value is 7.68.

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Answer:

(a) The line parallel to the y-axis that intersects the x-axis at (-6, 0)

(b) The line parallel to the x-axis that intersects the y-axis at (0, 6)

(c) The set of all points to the right of and on the y-axis

Answer:

(a) x = -6: a vertical line passing through (-6, y) for any value of y.

(b) y = 6: a horizontal line passing through (x, 6) for any value of x.

(c) 0 ≤ x: all points to the right of or on the y-axis, but not to the left of the y-axis.

Step-by-step explanation:

(a) x = -6:

(b) y = 6:

There are 9,000 numbers that have 7 in the thousands of places and are less than 54,000.

Consider the possible digits in the hundreds, tens, and one's places.

Thousands of places: There is only one possibility, which is 7.

Hundreds place: Any digit from 0 to 9 is possible.

Tens place: Any digit from 0 to 9 is possible.

One place: Any digit from 0 to 9 is possible.

Since the number is less than 54,000, the digit in the hundreds place cannot be 5.

So, there are 9 possible digits (0 to 9, except 5) for the hundreds place, and 10 possible digits (0 to 9) for the tens and one's places.

So, the total number of such numbers is:

9 x 10 x 10 x 10 = 9,000

Therefore, there are 9,000 numbers that satisfy the given condition.

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The length of the interior diagonal of the rectangular prism is approximately 141.4 centimeters.

To find the length of the interior diagonal of the rectangular prism, we need to use the Pythagorean theorem. The interior diagonal of the rectangular prism is the hypotenuse of a right triangle with legs equal to the length and width of the base and height of the rectangular prism.

Let's label the length, width, and height of the rectangular prism as l, w, and h, respectively. Then, the interior diagonal d can be found using the Pythagorean theorem as:

d² = l² + w² + h²

Substituting the given values, we get:

d² = 60² + 80² + 100²

Simplifying the expression:

d² = 3600 + 6400 + 10000

d² = 20000

Taking the square root of both sides, we get:

d ≈ 141.4 cm

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Complete question is:

A box in the shape of a rectangular prism has the dimensions shown. What is the length of the interior diagonal of the box? Round to the nearest tenth. Enter your answer in the box. A rectangular prism 60 centimeters wide, 80 centimeters long, and 100 centimeters tall. A diagonal d is drawn from the upper right rear corner to the lowest left front corner.

It would take about 2.6 years for the value of the account to reach $5,920, assuming no deposits or withdrawals are made.

We can use the formula for compound interest to solve the problem;

A = [tex]P(1+r/n)^{(nt)}[/tex]

where;

A is the amount after t years

P is principal (the initial amount invested)

r is annual interest rate (as a decimal)

n is number of times the interest is compounded per year

t is the time in years

In this case, we know that;

P = $4,900

r = 0.03 (3% expressed as a decimal)

n = 12 (interest is compounded monthly)

A = $5,920

We can solve for t by plugging in these values and solving for t;

$5,920 = $4,900[tex](1+0.03/12)^{12t}[/tex]

Divide both sides by $4,900;

1.20918367347 = [tex](1+0.03/12)^{12t}[/tex]

Take the natural logarithm of both sides;

ln(1.20918367347) = ln([tex](1+0.03/12)^{12t}[/tex])

Use the property of logarithms that allows us to bring the exponent down;

ln(1.20918367347) = 12t ln(1 + 0.03/12)

Divide both sides by 12 ln(1 + 0.03/12)

t = ln(1.20918367347) / (12 ln(1 + 0.03/12))

t ≈ 2.6 years

Therefore, it would take about 2.6 years.

--The given question is incomplete, the complete question is

"Ella invested $4,900 in an account paying an interest rate of 3% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $5,920?​"--

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We conclude that there is evidence to support the claim that mean wait time is less than 30 minutes

H0: The mean wait time is not less than 30 minutes

H1: The mean wait time is less than 30 minutes

The p-value is:

= 24.92 - 30 / 8.68 / ✓36

p = 0.0006

Based on the information, the null hypothesis will be rejected. There's not enough evidence to claim that the population means is less than 30.

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Answer:

45,971 books

Step-by-step explanation:

The library had 32,765 books this year. 1,578 books were ruined and 14,784 new books were purchased. To calculate the number of books in the library now, we need to subtract the number of ruined books from the original number of books and then add the number of new books purchased. Therefore, the number of books in the library now is:

32,765 - 1,578 + 14,784 = 45,971

So there are 45,971 books in the library now.

PLEASE MARK ME AS BRAINLIEST !!!

Answer: 45,971 books

Step-by-step explanation:

Started with 32765 books

1578 ruined    subtract

14784 new    add

32765-1578=31187

31187+14784  = 45,971

The equation of the circle from the given graph is (x + 2)² + (y - 2)² = 9.

The definition of a circle as a two-dimensional geometric shape is a closed curve with all points equally spaced from the centre, which is a fixed point. The radius of a circle is the separation between its centre and any point at its periphery. A circle is a form of ellipse with an equal length main and minor axis and no corners or edges. The design of wheels, gears, and circular buildings like domes and arches are just a few examples of how circles are used frequently in daily life. Circles also play a significant role in geometry, mathematics, and science.

The equation of a circle with center (h,k) and radius r is given by:

(x - h)² + (y - k)² = r²

Now, for the given center (-2, 2) we have:

(x - (-2))² + (y - 2)² = r²

(x + 2)² + (y - 2)² = r²

Now from the given figure r = 3 thus:

(x + 2)² + (y - 2)² = 3²

(x + 2)² + (y - 2)² = 9

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The smallest height of the towers is 3 cm.

We have,

Grace:

Kira's = 9 cm

Jake:

Blocks = 12 cm

Now, Kira and Jake build towers that are exactly the same height.

To find the smallest height we have to find the Least Common Multiple.

9 = 3 x 3

12= 2 x 2 x 3

So, LCM(9, 12) = 3

Thus, the smallest height of tower is 3.

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The value of arc length is,

Arc length = 70.65 radians

We have to given that;

Radius = 15 miles

And, Central angle = 3pi/2 radians

Since, We know that;

Arc length = Radius x Angle

Plug all the values,

Arc length = 15 x 3π/2

Arc length = 45π/2

Arc length = 45 x 3.14 / 2

Arc length = 70.65 radians

Thus, The value of arc length is,

Arc length = 70.65 radians

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Answer:

Let b = number of boys and g = number of girls.

g/b = 5/3, so g = (5/3)b

b + g = 136

b + (5/3)b = 136

(8/3)b = 136, so b = 136(3/8) = 51 boys, and g = 85 girls

There are 51 boys and 85 girls at the volleyball summer camp.

The ratio of boys to girls at the camp is 3 to 5. By applying this ratio to the total number of children at the camp (136), we find that there are 51 boys and 85 girls.

The question tells us that for every 3 boys at a camp, there are 5 girls. This means that the ratio of boys to girls is 3:5. This ratio tells us that out of every 8 (3+5) children, 3 are boys and 5 are girls.

Now it's mentioned there are 136 children in total. We divide total children by sum of the ratio to find out the number of boys and girls. 136 divided by 8 equals 17. This means there are 17 sets of 'every 8 children'.

To find the number of boys, multiply 3 (number of boys in one set) by 17 (total sets) and we get 51 boys. Using the same process for the girls, we multiply 5 (number of girls in one set) by 17 (total sets), resulting in 85 girls. Thus, among the 136 children at the camp, there are 51 boys and 85 girls.

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Before we can solve this question we need to create an expression to calculate 150$ discounted of 30%. The expression would be,

[tex]\text{T}=150\times(1-\text{r})[/tex]

Where:

Before we can use the formula we need to get the percent in decimal form by moving the decimal two digits to the left. Once we have that we can plug the values in the formula and solve for T.

30%   ⇔   0.30

[tex]\text{T}=150\times(1-\text{r})[/tex]

[tex]\text{T}=150\times(1-0.30)[/tex]

[tex]\text{T}=150\times0.70[/tex]

[tex]\boxed{\bold{T=105}}[/tex]

So we see that 150$ discounted of 30% is $105

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:   135%

Step-by-step explanation:

percents are parts out of the whole

In this case they want to know 81 is what part of 60.  81 is bigger than 60 so you are going to get something bigger than 100%

81/60

= 1.35

= 135%      move the decimal point over 2 times or multiply by 100

Answer: Question 1:

4 / 38 = 2/19

Alternative answer = 0.105

Question 2:

4 / 83 = 4/83

Alternative answer = 0.048

Step-by-step explanation:

Armed force and other for Henderson high school is greater than

Johnson High School.

The mode for each school is college.

Options F and G are the correct answer.

We have,

The number of students in Henderson High School.

Work = 96

College = 114

Armed forced = 48

Other = 42

The number of students in Johnson High School.

Work = 30

College = 40

Armed forced = 15

Other = 15

From the information,

The number of students in Work for Henderson High School is greater than Johnson High School.

Now,

Henderson High School:

Armed force and other = 48 + 42 = 90

Mode = college

Johnson High School.

Armed force and other = 15 + 15 = 30

Mode = college

Thus,

Armed force and other for Henderson high school is greater than

Johnson High School.

The mode for each school is college.

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Answer:

Short side: 9 cm
Long side: 12 cm

Hypotenuse: 15 cm

Step-by-step explanation:

9 squared= 81

12 squared= 144

144+81= 225

square root 0f 225= 15

9+6= 15

All sides follow the rules.

The value of the test statistic is -18.62.

In order to get value of the test statistic, we need to perform a hypothesis test.

Lets assume null hypothesis is 98% of adults have a cell phone and alternative hypothesis is that fewer than 98% of adults have a cell phone.

Using one-tailed z-test with significance level of 0.05, we will get test statistic with formula: z = (p - p) / sqrt(p * (1 - p) / n)

p = (0.90), p = (0.98 and n = (1062).

Plugging the values, we get:

z = (0.90 - 0.98) / sqrt(0.98 * (1 - 0.98) / 1062)

z = (0.90 - 0.98) /sqrt(0.00001845574)

z = (0.90 - 0.98) / 0.00429601443

z = -18.6219113794

z = -18.62

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Since you started at the origin of the coordinate plane and went 6 units to the left and 3 units up, the coordinates of your location is (-6, 3).

In Mathematics and Geometry, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image;

g(x) = f(x + N)

Conversely, the translation a geometric figure upward simply means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.

Based on the information provided, we have:

(x, y)                               →                  (x - 6, y + 3)

(0, 0)                              →                  (0 - 6, 0 + 3) = (-6, 3).

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With the help of probability concept, the expected winnings for this game is $2.17.

What is probability?

Probability is a branch of mathematics that deals with the study of random events or experiments. It is the measure of the likelihood or chance of an event or outcome occurring. Probability is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To find the expected winnings, we need to multiply each possible outcome by its respective probability and then sum all the products.

The possible outcomes are rolling a 1, 2, 3, 4, 5, or 6.

The probabilities of rolling each number are equal since we are assuming the die is fair, so the probability of rolling any number is 1/6.

The payoffs for rolling each number are as follows:

$8 for a 6 (probability 1/6)

$4 for a 5 (probability 1/6)

$1 for a 4 (probability 1/6)

$0 for a 1, 2, or 3 (probability 3/6)

Therefore, the expected winnings can be calculated as follows:

Expected winnings = (8 x 1/6) + (4 x 1/6) + (1 x 1/6) + (0 x 3/6)

Expected winnings = 1.33 + 0.67 + 0.17 + 0

Expected winnings = $2.17

Therefore, the expected winnings for this game is $2.17.

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Each switch has 2 possible positions ("+" or "-"), so the total number of ways to set all 10 switches is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2, which is equal to 1024. Therefore, there are 1024 ways to set the switches for the garage door opener.