Look at the figure shown. Which angle is obtuse?
Angle CDA.
Angle BAD.
Angle CBA.
Angle DAB.
A
60
B
120
120
C
60
D

Answer:

  30.0 ft

Step-by-step explanation:

You want the length of a pole whose shadow is 20 ft long when the angle of elevation of the sun is 62° and the pole is tilted 8° away from the sun.

Referring to the attached diagram, we see that the interior angle at B of triangle ABC is 90° -8° = 82°. This makes the interior angle at A ...

  A = 180° -82° -62° = 36°

The law of sines tells us side lengths are proportional to the sines of the opposite angles:

  c/sin(C) = a/sin(A)

  c = a×sin(C)/sin(A) = 20×sin(62°)/sin(36°) ≈ 30.043 . . . feet

The length of the pole is about 30.0 feet.

The temperature of Srinagar on Wednesday was -3°C.

If the temperature was -5°C on Monday and dropped by 2°C on Tuesday, we can subtract 2 from -5 to get:

-5°C - 2°C = -7°C

So the temperature of Srinagar on Tuesday was -7°C.

If the temperature on Wednesday rose by 4°C from the temperature on Tuesday, we can add 4 to -7°C to get:

-7°C + 4°C = -3°C

So the temperature of Srinagar on Wednesday was -3°C.

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The complete question:

At Srinagar temperature was -5°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?

The volume of this sphere is 1607. 68 in³

It is important to note that the formula that is used to calculate the volume of a sphere is expressed as;

V = 4/3 πr3

Given that the parameters are;

From the information given,

Substitute the values, we have;

Volume = 4/3 × 3.14 ×8³

Find the cube values, we get;

Volume = 4/3 × 3.14 × 512

Multiply the values

Volume = 2143. 57 in³

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The difference between the median math test score, as shown by the ox plots, is: 12.5.

The median of a data set is displayed in a box plot as the value that is at the vertical line that divides the rectangular box. This is also 50% mark of the data set.

Thus, the data set for afternoon, as shown in the box plot has a median that is 75, while the median of the data set for morning is 87.5.

Find the difference of their medians:

Difference of their medians = 87.5 - 75 = 12.5.

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The volume of the cone is  37.70 cm³.

The volume of the cone is calculated as follows;

V = ¹/₃πr²h

where;

The radius of the cone is calculated by applying the following formula;

r = √ (5² - 4²)

r = 3 cm

The volume of the cone is calculated as;

V = ¹/₃πr²h

V = ¹/₃π(3)²(4)

V = 37.7 cm³

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Answer:

632.83mm²

Step-by-step explanation:

Applying Pythagorean theorem to triangle SOH

SH² = SO² + OH²

SH = [tex]\sqrt{(15.4)^2+(7.2)^2}=17mm[/tex]

Since the base of the pyramid is a regular pentagon, angle OAH
is 108°/2 = 54°.

AH = 7.2/tan 54° = 5.23mm

So AB = 2AH = 10.46mm

The area of triangle SAB is:

A1 = 1/2 × SH × AB = 1/2 × 17 × 10.46 = 88.91mm²

The area of all triangles is

A2 = 5 × A1 = 5 × 88.91 = 444.55mm²

The area of the base is:

A3 = (perimeter × apothem)/2 = (5 × 10.46 × 7.2)/2 = 188.28mm²

The surface area of the pyramid is:

A2 + A3 = 444.55 + 188.28 = 632.83mm²

Step-by-step explanation:

the surface area is the sum of the base area (pentagon) and the 5 side triangles (we only need to calculate one and then multiply by 5, as they are all equal).

these side triangles are isoceles triangles (the legs are equally long).

the usual area formula for a pentagon is

1/2 × perimeter × apothem

the apothem is the minimum distance from the center of the pentagon to each of its sides.

in our case this is 7.2 mm.

how to get the perimeter or the length of an individual side of the pentagon ?

if the apothem of a pentagon is given, the side length can be calculated with the formula

side length = 2 × apothem length × tan(180/n)

where 'n' is the number of sides (5 in our case). After getting the side length, the perimeter of the pentagon can be calculated with the formula

perimeter = 5 × side length.

so, in our case

side length = 2 × 7.2 × tan(180/5) = 14.4 × tan(36) =

= 10.4622124... mm

perimeter = 5 × 10.4622124... = 52.31106202... mm

area of the pentagon = 1/2 × perimeter × apothem =

= 1/2 × 52.31106202... × 7.2 = 188.3198233... mm²

now for the side triangles.

the area of such a triangle is

1/2 × baseline × height

baseline = pentagon side length

height we get via Pythagoras from the inner pyramid height and the apothem :

height² = 7.2² + 15.4² = 51.84 + 273.16 = 289

height = 17 mm

area of one side triangle =

1/2 × 10.4622124... × 17 = 88.92880543... mm²

all 5 side triangles are then

444.6440271... mm²

and the total surface area is then

444.6440271... + 188.3198233... = 632.9638504... mm²

≈ 632.96 mm²

The p-value of 4.91541E-15 (or 4.91541 x 10^-15) is considerably beneath the conventional significance level of 0.05 employed in statistical hypothesis testing.

In hypothesis testing, the p-value symbolizes the probability of detecting the test statistic (or an even larger value) under the null hypothesis. A p-value of 0.05 or below often appears statistically relevant, suggesting powerful evidence contrary to the null hypothesis.

Therefore, a p-value of 4.91541E-15 being far less than 0.05 implies very compelling evidence against the null hypothesis.

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Step-by-step explanation:

you can find the answer by vertical opposite angle

if the value of x is computed and it's equal to 78 you will find the answer

78=(12x+18)^

78=(12×5+18)

78=(60+18)

78=78 the problem is solved

may u get branliest please please

Answer:

We can use the formula to find the length of a circular arc given the measure of the central angle and the radius:

Length of arc = (central angle measure / 360) x 2πr

where r is the radius of the circle.

Given that the central angle measure is 40° and the length of the arc is 6 cm, we can set up the equation:

6 = (40/360) x 2πr

Simplifying the fraction and solving for r, we get:

6 = (1/9) x 2πr

r = 9 x 6 / 2π

r = 27/π

So the radius of the circle is 8.59 cm (rounded to two decimal places).

Answer:

m = 476

Step-by-step explanation:

m + 310 = 786

(Subtract 310 from both sides.)

m = 786 - 310

(Subtract 310 from 786 to get 476)

m = 476

The summary of Angle Relationships in a Circle is given.

The following is an overview of angle relationships in a circle:

The vertex of a central angle is the center of the circle. A central angle's length equals the length of the arc it crosses.

Inscribed angle: An angle with a circle as its vertex and sides that intersect two separate arcs. An inscribed angle has half the length of the arc it intersects.

Tangent-chord angle: A tangent-chord angle is generated when a tangent and a chord cross at the point of tangency. The length of this angle is half the length of the intercepted arc.

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The zeros are not the factors of the expression using the synthetic method

The expression is given as

x⁴ - 4x² + 10x + 13

Testing the factors, we have

(x, y) = (2, 0)

The synthetic set up is

2 |   1  0  -4   10   12

    |__________

Bring down the first coefficient, which is 1 and repeat the process

2 |   1  0  -4   10   12

    |___2_4__0__20__

       1   2   0  10    32

This has a remainder of 32

So, (2, 0) is not a factor

(x, y) = (1, 0)

The synthetic set up is

1 |   1  0  -4   10   12

    |__________

Bring down the first coefficient, which is 1 and repeat the process

1  |   1  0  -4   10   12

    |___1__1__-3_7__

       1   1   -3    7    19

This has a remainder of 19

So, (1, 0) is not a factor

(x, y) = (-1, 0)

The synthetic set up is

-1  |   1  0  -4   10   12

    |__________

Bring down the first coefficient, which is 1 and repeat the process

-1  |   1  0  -4   10   12

    |__-1__1__3__13__

       1  -1   -3    13   25

This has a remainder of 25

So, (-1, 0) is not a factor

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Answer:

124

Step-by-step explanation:

To find the number that should be added to the data so that the range of the data is 63, we first need to find the current range of the data.

The range of a set of data is the difference between the largest and smallest values in the set.

So, to find the current range of the data, we need to subtract the smallest value from the largest value:

Range = largest value - smallest value

Range = 97 - 61

Range = 36

This means that the current range of the data is 36.

To increase the range to 63, we need to add a number that is 63 - 36 = 27 larger than the current range.

To do this, we can add 27 to the largest value in the data set, which is 97:

97 + 27 = 124

So, we should add 27 to the data set to increase the range to 63.

Therefore, the complete set of data would be:

78, 61, 95, 77, 85, 97, 124

Check:

To find the range of the data set 78, 61, 95, 77, 85, 97, 124, we need to subtract the smallest value from the largest value:

Range = largest value - smallest value

Range = 124 - 61

Range = 63

Therefore, the range of the data set 78, 61, 95, 77, 85, 97, 124 is 63.

The volume of the rectangular prism which is as described in the task content is; 67½ cm³.

It follows from the task content that the value of the rectangular prism which is as described is required to be determined.

Since the rectangular prism has width as six centimeters, the length as two and a half centimeters and the height as four and a half centimeters;

Volume = l × w × h

Volume = 2½ × 6 × 4½

Volume = 5/2 × 6 × 9 / 2

Volume = 67½ cm³.

Ultimately, the volume of the prism is; 67.5 cm³.

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The equivalent expression for 8y + 12 + 2y + 8 will be 10y + 20.

The number of problems that she get wrong is 4.

The days that Jared work to make 20 bird houses is 15 days.

The equivalent expression for 8y + 12 + 2y + 8 will be:

= 8y + 12 + 2y + 8

= 10y + 20

The number of problems that she get wrong is:

= (1 - 84%) × 25

= 0.16 × 25

= 4.

The days that Jared work to make 20 bird houses is:

= 3/4 × 20

= 15 days.

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Write an equivalent expression for 8y + 12 + 2y + 8

Maria’s math test had 25 questions. She got 84% correct. How many problems did she get wrong?

Jared made 4 bird houses in 3 days. How many days will Jared work to make 20 bird houses?

The probability that he plays a rock song than a hip hop song is greater than 0.1. The Option B is correct.

Probability helps to find out the likelihood of the occurrence of an event by measuring the chance of an event happening and is equal to the number of favorable events divided by the total number of events.

Given that:

Total of songs = 40

Prob (playing rock) = 15/40

Prob (playing hip-pop) = 11/40

How much greater probability he plays a rock song than a hip hop song will be:

= 15 / 40 - 11/40

= 15 - 11 / 40

= 4/40

= 1/10

= 0.1

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1560 g.

To convert 1.56 kg to g, we can use the conversion factor 1 kg = 1000 g:

1.56 kg = 1.56 x 1000 g = 1560 g

Therefore, the answer is 1560 g.

The proportion of the babies born

Given that

Uniform Distribution from 1 – 53

This means that

a = 1 and b = 53

So, we have

Mean = (a + b)/2 = (1 + 53)/2 = 27

Standard deviation = √[(b – a)² / 12] = √[(53 – 1)² / 12] = 15

After the 40th week of the year

The z-score is calculated as

z = (x - mean)/Standard deviation

So, we have

z = (40 - 27)/15 = 0.8667

So, we have

Proportion = P(z > 0.8667)

Proportion = 80.7%

Before the 10th week of the year

z = (10 - 27)/15 = -1.133

So, we have

Proportion = P(z < -1.133)

Proportion = 12.9%

Between the 10th and 40th week of the year

This is calculated as

Proportion = (-1.133 < z < 0.8667)

So, we have

Proportion = 67.8%

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The algebraic expression is represented as 12 - 4x

It is important that we note that algebraic expressions are those expressions that are made up of some variables, certain terms, coefficients, factors and constants.

These algebraic expressions are also identified with the presence of arithmetic operations, such as;

From the information given,

Let the number by x

We then have;

The coefficient is 4

The constant is 12

The variable is x

Substitute the terms

12 - 4x

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The expected profit for the first mall is $425,000.

To calculate the expected profit for the first mall, we need to multiply the profit for each outcome by its probability, and then add up the results.

Let S denote success and F denote failure for the first mall.

Then the expected profit is:

Expected profit for the first mall = (probability of success) × (profit for success) + (probability of failure) × (profit for failure)

Expected profit for the first mall = (1/2) × $1,275,000 + (1/2) × (-$425,000)

Expected profit for the first mall = $637,500 - $212,500

Expected profit for the first mall = $425,000

Therefore, the expected profit for the first mall is $425,000.

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Answer:

8 ft

Step-by-step explanation:

Area of a triangle=1/2*base*height

You know the area of the triangle and the height, so you can set up an expression to solve for the base

48=1/2*base*12

4=1/2*base

base=8ft

Check: A=1/2*8*12, A=48 ft²

The probability that either event will occur to the nearest hundredth would be = 0.9

To calculate the probability of the given events, the sample space should be generated and followed by the probability of each sample space generated.

That is;

P(A) = 14/18 = 0.78

P(B) = 10/18 = 0.56

P(A and B) = 0.78×0.56 = 0.4368

Therefore ;

P(A or B)= 0.78+0.56-0.4368

= 1.34- 0.4368

= 0.9

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The y- intercept for both function is 0 and 5.8.

We have First function

y= [tex]9^x[/tex]

Now , the y intercept of the equation is when x = 0

So , when x = 0

y= [tex]9^0[/tex]

y= 0

and, the second function is

y= [tex]9^{0.8[/tex]

y= 5.799

Hence, second function have intercept 5.8.

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The slope of the line that cuts through the points (1, -5) and (3, 5) is equal to 2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (5 - (-5))/(3 - 1)

Slope (m) = (5 + 5)/(2)

Slope (m) = 10/2

Slope (m) = 2.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 2.

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There is enough data to indicate that Jordanian children are at risk of anemia.

The null hypothesis is that the true mean hemoglobin level for Jordanian children is greater than or equal to 12 g/dl, and the alternative hypothesis is that it is less than 12 g/dl.

Using the P-value method:

The test statistic for the one-sample t-test is given by:

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the population means (here, μ = 12), s is the sample standard deviation, and n is the sample size.

Substitute the given values,

t = (11.3 - 12) / (1.6 / √50) = -2.98

Using a t-distribution table with 49 degrees of freedom (df = n - 1), find that the p-value for this test is approximately 0.002.

Since the p-value is less than the significance level of α = 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that Jordanian children are at risk of anemia.

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Answer:

I think it’s

False

True

True

True

True

False

True

False

Answer:

84%

Step-by-step explanation:

The total is 25 students. (21+4)

The students that voted are 21

21/25 = 0.84

The profession that would earn that amount more than a bank teller is Office Clerk.

The profession that would earn $1,151,700 in 30 years is Bookkeeper.

The profession that will earn  $828,600 over a 20-year career is Truck Driver.

The profession that earns $136,200 more than a fire fighter over a period of 30 years is Electrician

The 15 year difference between bank teller and office clerk is:

= ( 30, 850 x 15 ) - ( 27, 260 x 15 )

= $ 53, 850

The earnings of a Bookkeeper in 30 years is:

= 38, 390 x 30

= $ 1, 151, 700

The earnings of a Truck driver in 20 years is :

= 41, 430 x 20

= $ 828, 600

The difference between earnings of Fire fighter and Electrician over 30 years is:

= ( 52, 570 x 30 ) - ( 48, 030 x 30 )

= $ 136, 200

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