Solve the equation.


3p/8-13=-25

Answer:

B because it is close to 30

Step-by-step explanation:

Answer:

The correct answer is option A   17.8°

Step-by-step explanation:

From the figure attached with this answer,

We can see a perpendicular from B to side AC

To find BD

In triangle BDC, its angles are 30°, 60° and 90°

Therefore the sides are in the ratio 1 :√3 : 2

Here BC = 11

BD : DC : BC = 1 :√3 : 2 = 11√3/2 : 11/2 : 11

Therefore BD = 11/2

To find the value of  m<A

We have

Sin ∅ = Opposite side /Hypotenuse

AB = 18 and BD = 11/2

Sin A = BD/AB =(11/2)/18 = 11/36 = 0.3055

m<A = Sin⁻¹(0.3055) = 17.79 ≈ 17.8°

Therefore the correct answer is option A  17.8°

Let x be the unknown number. One fifth of this number is x/5, one fourth of this number is x/4. So, we have

[tex]\dfrac{x}{4}-\dfrac{x}{5} = \dfrac{5x-4x}{20} = \dfrac{x}{20}[/tex]

We know that this difference equals 9, so we have

[tex]\dfrac{x}{20}=9[/tex]

Multiply both sides by 20 to get

[tex]x=180[/tex]

Answer:

The value of cosФ = -√5/3

Step-by-step explanation:

∵ sinФ = 2/3

∵ tanФ is less than 0

* Lets think about that:

 the value of sin is positive and the value of tan is negative

 according to ASTC rule:

 - All are positive in the first quadrant

 - sin only positive in the second quadrant

 - tan only positive in the third quadrant

 - cos only positive in the fourth quadrant

∴ Angle Ф lies on the second quadrant

∴ The value of cosФ is less than 0

∵ sin²Ф + cos²Ф = 1

∵ sinФ = 2/3

∴ (2/3)² + cos²Ф = 1

∴ cos²Ф = 1 - 4/9 = 5/9

∴ cosФ = ± √5/3

∵ Angle Ф lies on second quadrant

∴ cosФ = -√5/3

The cosine of the angle θ, given that sine θ is 2/3 and tangent θ is negative, is -√(5/9) since the angle is in the second quadrant.

If the sine of an angle (θ) is 2/3 and the tangent of that angle is less than zero, this indicates that the angle is in the second or fourth quadrant, where tangent values are negative. However, since sine is positive, the angle θ must be in the second quadrant. To find the cosine of θ, we can use the Pythagorean identity: sin² θ + cos² θ = 1. Substituting the sine value, we get (2/3)² + cos² θ = 1, which simplifies to 4/9 + cos² θ = 1. Solving for cosine gives us cos² θ = 1 - 4/9 = 5/9. The cosine value itself will be negative because cosine is negative in the second quadrant, so cos θ = -√(5/9).

Answer:

20cm or A

Step-by-step explanation:

pythagorean theorem

25^2=15^2+b^2

625=225+b^2

b^2=400

b=20

A because it is the number in between 15 and 25 because the line is shorter

I think $18.50 would earn you the most money.

The first choice would earn you $33,350

The second choice would earn you $32,000

The third choice would earn you $33,670

I think the last choice would earn you $31,500

Hope this helps.

Answer:

Step-by-step explanation:

Givens

$17.50 per hour and $1,500 bonus at the end of the year, that is, at the ends of the 52 weeks.

If you work 35 hours per week for 52 weeks, with this plan, you gain

[tex]17.50 \times 35 = \$ 612.50[/tex]

Then, after 52 weeks: [tex]\$612.50 \times 52=\$ 31,850[/tex]

So, with the first plan, you make $31,850 + $1,500 = $33,350.

Just $32,000 per year. It's a little bit better than the first situation.

$18.50 per hour.

So, per week would be: [tex]18.50 \times 35 = \$647.50[/tex]

After 52 weeks you make: [tex]\$647.50 \times 52=\$33,670[/tex]

So, with the third plan, you make $33,670.

$30,000 per year with a 5% bonus, which mean

[tex]30,000 + 0.05(30,000)=30,000+1,500=31,500[/tex]

So, with this plane you make $31,500 a year.

Therefore, as you can deduct, the best option is the third plan, $33,670 per year.

Answer:

$791

Step-by-step explanation:

Find the equation of the line passing thru  (30, 1,181) and (44, 1,363),   The y-intercept of this equation will answer this question:  it represents the annual golf pass.

Moving from (30, 1,181) to (44, 1,363), we see x increasing by 14 from 30 to 44 and y increasing by  182   from 1181 to 1363.

Thus, the slope of this line is m = rise / run = 182 / 14 = 13.

Subst. the knowns (30, 1,181) and m = 13 into the standard equation for a straight line in slope-intercept form, y = mx + b, we get:

1181 = 13(30) + b.  Then 1181 - 390 = 791.

The flat fee is $791, payable at the beginning of each year.

Answer:

The answer is $760

Step-by-step explanation:

First, find the rate of change, or slope, from the two given points.

Next, find the equation for the linear model using the slope and a point.

The initial value is the value of y when x equals 0.

In this case, the initial value is the flat fee for the annual golf pass.

Therefore, the flat fee for the annual golf pass is $760.

Answer:

case 1) [tex]z=10[/tex]

case 2) [tex]z=5/32[/tex]

Step-by-step explanation:

case 1) we know that

Using proportion

[tex]\frac{1}{z}=\frac{(4/5)}{8}[/tex]

solve for z

[tex]\frac{1}{z}=\frac{(4/5)}{8}\\ \\z(4/5)=8\\ \\z=8*5/4\\ \\z=10[/tex]

case 2) we know that

Using proportion

[tex]\frac{1}{z}=\frac{4}{5/8}[/tex]

solve for z

[tex]\frac{1}{z}=\frac{4}{5/8}\\ \\4z=5/8\\ \\z=5/32[/tex]

Answer:

Tasha made a mistake in Step 4

Step-by-step explanation:

She made a mistake in step 4

When rewriting the value for  4^(-4)

She needed to write

(1/256) =   4^(-4)

Instead, she wrote

(1/256) =   -1/4^(-4)

-1/4^(-4) = -256 ≠ (1/256)

Answer:

Step-by-step explanation:

Let the two numbers be x and y

x + y = 6

x - y = 36       Add the two equations.

2x = 42          Divide by 2

2x/2 = 42/2

x = 21

x + y = 6         Substitute for x

21 + y = 6        Subtract 21

21-21 + y = 6-21

y = - 15

Answer:

option C

9 x 9 x 9 x 9 x 9  

Step-by-step explanation:

Given in the question the expression

[tex]9^{5}[/tex]

The exponent corresponds to the number of times the base is used as a factor.

in which base = 9

              exponent = 5

9 x 5

45

[tex]5^{9}[/tex]

[tex]9^{5}[/tex]

[tex]9^{5} x 5^{9}[/tex]

Answer: Christina weighs 98 pounds.

Step-by-step explanation: The formula to solve this problem is x + 17 + x = 179, where x equals Sarah’s weight.

X + 17 + x = 179

First you need to combine the x values:

2x + 17 = 179

Next, subtract 17 from both sides:

2x = 162

Finally, divide both sides by 2:

X = 81

Sarah’s weight is 81 pounds and Christina weighs 17 pounds more, which is 98 pounds. You can double check your work by adding both of their weights (98 + 81) to make sure that your answer is correct.

Final answer:

By setting up a system of equations with the given information, we can solve for Christina's weight. Christina weighs 125 pounds.

Explanation:

To determine how much Christina weighs, we can set up an equation based on the information given. Let's define Sarah's weight as 's' and Christina's weight as 'c'. According to the question, Christina weighs 17 pounds more than twice Sarah's weight. So we can write the equation as:

c = 2s + 17

The combined weight of Christina and Sarah on the freight scale is 179 pounds. We represent this with another equation:

c + s = 179

Now we have a system of two equations:

Substituting the expression for 'c' from the first equation into the second equation gives us:

(2s + 17) + s = 179

Combining like terms, we have:

3s + 17 = 179

Moving 17 to the other side by subtracting 17 from both sides:

3s = 179 - 17

3s = 162

Dividing both sides by 3 to find Sarah's weight:

s = 162 / 3

s = 54

Now that we know Sarah weighs 54 pounds, we can find Christina's weight using the first equation:

c = 2(54) + 17

c = 108 + 17

c = 125

So, Christina weighs 125 pounds.

Answer:

45

Step-by-step explanation:

Decreasing by 25% means that there is 25% less of last years amount or 0.25x less. It also means that this year there is only 75% of what was last year actually in the lake or 0.75x. Since last year, there were 60 fish, this means this year there is 0.75(60) = 45. This year has 45 fish.

Answer:

45

Step-by-step explanation:

Answer:

[tex]\large\boxed{\ln e^A=A}[/tex]

Step-by-step explanation:

[tex]Use\\\\\log_ab^n=n\log_ab\\\\\log_aa=1\\\\\ln a=\log_e a\to\ln e=1\\====================================\\\\\ln e^A=A\ln e=A(1)=A[/tex][/tex]

Answer: [tex]10\sqrt{2}units[/tex]

Step-by-step explanation:

You must apply the Pytagorean theorem, which is shown below:

[tex]a^2=b^2+c^2[/tex]

Where:

a is the hypotenuse and b and c are the legs of the triangle.

Then, if you know the lenght of the legs of the triangle, you can solve for the hypotenuse.

Therefore, keeping the above on mind, you obtain the following result:

[tex]a=\sqrt{b^2+c^2}[/tex]

[tex]a=\sqrt{(10units)^2+(10units)^2}\\a=10\sqrt{2}units[/tex]

The length of the hypotenuse of the triangle is 10√2 units

The triangle is a right angle triangle.

Right angle triangles are triangle that has one of its angles as 90 degrees.

Using Pythagoras theorem, we can find the length of the hypotenuse with the length of the two legs.

Therefore,

c² = 10² + 10²

c² = 100 + 100

c = √200

c = 10√2

learn more on right angle triangle here: https://brainly.com/question/2796771?referrer=searchResults

➷ First find the number of scans produced per second

To do this, multiply the number of scans by 30:

525 x 30 = 15750

So, there are 15750 scans produced per second

You need the value for 30 seconds, so multiply by 30 again

15750 x 30 = 472500

Your answer would be 472500

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

C / (2 pi) = r

Step-by-step explanation:

C = 2 pi r

Divide each side by 2 pi

C / (2 pi) = 2 pi r/ (2 pi)

C / (2 pi) = r

Answer:

less 13 gallons equals 52 quarts

Step-by-step explanation:

Equal to. There are 4 quarts in 1 gallon. So 16x4=64

Answer:

This graph is reflected over the x-axis

Step-by-step explanation:

This is because the negative is a coefficient in front. This causes the graph to flip, which is the same as a reflection over the x-axis

Answer:

A

Step-by-step explanation:

Since we're dealing with the b value here, we are talking about an x axis reflection.

Answer:

(2,-4)

Step-by-step explanation:

it is a minimum because as you can see the lowest is at the point of (2,-4)

Answer:

(2,-4)

Step-by-step explanation:

Answer: 450 miles

Step-by-step explanation:

3 inches / 1 inch = 3 times 150 miles = 450 miles

Answer:

m=-13

Step-by-step explanation:

What you do is you minus 45 from each side to get.

m=-13 as your answer.

Answer: -13

Step-by-step explanation:

Subtract 45 from 32 u get -13 = m

Answer:

2x - y = 13

Step-by-step explanation:

To write the equation of a line use the formula [tex]y - y_1 = m(x-x_1)[/tex].

Substitute m = 2 and (4,-5).

[tex]y --5 = 2(x-4)\\y + 5 = 2(x - 4)\\y + 5 = 2x - 8\\y = 2x -13\\-2x + y = -13\\2x - y = 13[/tex]

The break ended at 4pm when he was at 15 km.

The ride ended at 6pm when he was at 45 km.

From 4 to 6pm he rode 45 - 15 = 30 km.

Answer: it would be 30 kilometer

Step-by-step explanation:

45-15=30

Answer:

4y^(2)+14y+31

Step-by-step explanation:

First you need to do (y+7)(y+7)

y^2+7y+7y+49

y^2+14y+49

Add it all together

y^2+14y+49+3y^2-15

4y^(2)+14y+31

Answer:

An angle showing a turn through 1/8 of a circle is smaller

Step-by-step explanation:

we know that

A complete circle represent 360°

so

An angle showing a turn through 1/8 of a circle is

[tex](360\°)*(\frac{1}{8})=45\°[/tex]

An angle showing a turn through 1/3 of a circle is

[tex](360\°)*(\frac{1}{3})=120\°[/tex]

therefore

An angle showing a turn through 1/8 of a circle is smaller

Answer:

1/8 is smaller because it equals 45 degrees

1/3 is bigger because it equals 120 degees

Answer: 24 meters.

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

[tex]P=2l+2w[/tex]

Where l is the lenght and w is the width.

The perimeter of the original rectangle  is 88 m, then:

[tex]88=2l+2w[/tex]      [EQUATION 1]

Where l is the length of the original rectangle

 You know that if the width were doubled and the length were increased by 12 m, the perimeter would be 152 m. Therefore the new length is:

[tex]l+12[/tex]

The new width is:

[tex]2w[/tex]

Susbtitute into the equation of the perimeter and solve for w:

[tex]152=2(l+12)+2(2w)\\4w=152-(2l+24)[/tex]

 [tex]w=\frac{128-2l}{4}[/tex]      [EQUATION 2]

Substitute the Equation 2 into Equation 1 and solve for the length, as you can see below:

[tex]88=2l+2(\frac{128-2l}{4})[/tex]

[tex]88=2l+2(\frac{128-2l}{4})\\88-2l=\frac{128-2l}{2}\\\\176-4l=128-2l\\176-128=4l-2l\\\frac{48}{2}=l\\\\24=l[/tex]

Therefore, the length of the original rectangle is 24 m.

Answer:

Length  of original rectangle = 24 m

Step-by-step explanation:

Perimeter of rectangle

P = 2(l + b)

l - length and b - width

It is given that,the perimeter of a rectangle is 88 m. If the width were doubled and the length were increased by 12 m, the perimeter would be 152 m

Perimeter of original rectangle = 88 m

2(l + b) = 88

l + b = 44

b = 44 - l

To find length and width

length l = l + 12  and width = 2(44 - l) then,

Perimeter = 152 m

we can write,

2( l + 12 + 2(44 - l)) = 152

l + 12 + 88 - 2l = 152/2 = 76

100 - l = 76

l = 100 - 76 = 24

Therefore length = 24 m

width = 44 - l = 44 - 24 - 20 m

Rational number since a rational number is Any integer

Final answer:

The probability of Robert eating two mint sticks consecutively from a bag of candy is 3/95, which is found by multiplying the individual probabilities of selecting a mint stick on the first and second draw.

Explanation:

The question involves calculating the probability that the first two pieces of candy Robert eats are both mint sticks. To find this probability, follow a step-by-step process to consider all possible outcomes.

Step 1: Probability of first mint stick

Initially, Robert has 20 pieces of candy with 4 being mint sticks. So, the probability of picking a mint stick first is:

4 mint sticks / 20 total pieces = 1/5 or 0.20.

Step 2: Probability of second mint stick

After eating one mint stick, there remain 3 mint sticks out of 19 total pieces. Thus, the probability now becomes:

3 mint sticks / 19 total pieces = 3/19.

Step 3: Combined probability

To find the probability of both events happening consecutively, multiply the separate probabilities:

(1/5) * (3/19) = 3/95, which simplifies to 0.0316, or about 3.16% chance.

Therefore, the correct answer is C. 3/95.

Answer:

1. 121 π  unit²

2. 143°

3. 151 unit²

Step-by-step explanation:

1.

Area of a circle is given by the formula  A = πr²

where

A is the area,

r is the radius of the circle

From the given diagram, we can see that the radius is 11, hence the area will be:

[tex]A=\pi r^2\\A=\pi (11)^2\\A=121\pi[/tex]

The answer is  [tex]121\pi[/tex] units^2

2.

The unshaded secctor and the shaded sector equals the circle. We know that circle is 360°. The unshaded sector has an angle of 217°. So the shaded part will be 360 - 217 = 143°

The measure of the central angle of the shaded sector is 143°

3.

Area of a sector is given by the formula  [tex]A=\frac{\theta}{360}*\pi r^2[/tex]

Where

[tex]\theta[/tex] is the central angle of the sector (in our case it is 143°)

r is the radius (which is 11)

Plugging in all the info into the formula we have:

[tex]A=\frac{\theta}{360}*\pi r^2\\A=\frac{143}{360}*\pi (11)^2\\A=150.99[/tex]

rounding to the nearest whole number, it is 151 units^2