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Answer:

483

Step-by-step explanation:

840 minus 357 is 483

Answer:

0.04233 ounces of medicine in a day

Step-by-step explanation:

Answer:

20.19°

Step-by-step explanation:

Find the diagram to the question attached. We are to look for <CAB

Applying sine rule on ΔABC:

[tex]\frac{4.5}{sin15^0} = \frac{6}{sin<CAB}[/tex]

cross multiply

[tex]4.5 * sin<CAB =6 sin15^0\\\\sin<CAB = \frac{6sin15^0}{4.5}\\ \\sin<CAB = \frac{6*0.2588}{4.5}\\ \\sin<CAB = \frac{1.5529}{4.5}\\\\sin<CAB = 0.3451\\\\<CAB = sin^{-1}0.3451\\[/tex]

[tex]<CAB = 20.19^0\\[/tex]

Hence the angle <CAB is 20.19°

The angle ∠CAB is 20.19° and the distance (d) Ollie is from the entrance to his house when he first activates the sensor is 5.77 m.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

Ollie has installed security lights on the side of his house that is activated by a sensor.

The sensor is located at point C directly above point D.

The area covered by the sensor is shown by the shaded region enclosed by triangle ABC.

The distance from A to B is 4.5 m and the distance from B to C is 6 m.

The angle ACB is 15°.

The ∠CAB is ∠A.

We know that the sine rule

[tex]\dfrac{a}{\sin A} =\dfrac{b}{\sin B} = \dfrac{c}{\sin C}[/tex]

We have

[tex]\dfrac{AB}{\sin C} \ \ = \dfrac{BC}{\sin A} = \dfrac{AC}{\sin B}\\\\\\\dfrac{4.5}{\sin 15^o} = \dfrac{6}{\sin A} = \dfrac{b}{\sin B}[/tex]

From the first two, we have

[tex]\dfrac{4.5}{\sin 15^o} = \dfrac{6}{\sin A} \\\\\sin A = \dfrac{6}{4.5} \times \sin 15^o\\\\A \ \ \ \ = 20.19^o[/tex]

We know that the sum of the angle is 180 degrees. Then we have

    ∠A + ∠B + ∠C = 180°

20.19° + ∠B + 15° = 180°

                      ∠B = 144.81°

Then the value of b will be

[tex]\dfrac{4.5}{\sin 15^o} = \dfrac{b}{\sin 144.81^o}\\\\\\b \ \ \ = 10.02[/tex]

Then the distance (d) Ollie is from the entrance to his house when he first activates the sensor will be

d = b × sin 144.81°

d = 10.02 × sin 144.81°

d = 5.77 m

More about the trigonometry link is given below.

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Answer:

48 , 132

Step-by-step explanation:

Let smaller angle = x

Larger angle = 3x - 12

x & (3x - 12) are supplementary

So, x + 3x - 12 = 180°

          4x - 12 = 180

                  4x = 180 +12

                   4x = 192

                     x = 192/4

x = 48°

Larger angle = 3*48 - 12 = 144 - 12 = 132

Answer: The measure of the smaller angle is 48,and the larger angle is 132.

Step-by-step explanation:

Answer: ∠2, ∠6 is your answer. If that's not the answer than ∠7, ∠5 might be your answer.

hope it helps

The volume of the hexagonal prism is the amount of space in it.

From the complete question, we have:

Length (l) = 8

Height (h) = 5

The surface area of the hexagonal prism is:

[tex]A=6lh+3l^2\sqrt 3[/tex]

So, we have:

[tex]A=6*8*5+3*5^2\sqrt 3[/tex]

Evaluate

[tex]A = 369.9[/tex]

Hence, the surface area is 369.9 square feet

The volume of the hexagonal prism is:

[tex]V = \frac{3\sqrt 3}{2} * l^2h[/tex]

So, we have:

[tex]V = \frac{3\sqrt 3}{2} * 8^2 * 5[/tex]

Evaluate

[tex]V = 831.4[/tex]

Hence, the volume is 831.4 cubic feet

Read more about surface area and volume at:

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Answer:

C.

Step-by-step explanation:

Do 10 to the 2nd power (which is 100) the multiply it by the 8 then you get 800!

Answer:

irrational

Step-by-step explanation:

Answer:

24weeks

Step-by-step explanation:

So if she spends 5$ three times a week she spends 15$ a week

She babysits once a week for 40$

That means that she saves 25$ from babystitting each week

As she already has saved 200$, she only lacks 600$ for the purchase

600$ / (25$/week) = 24 weeks

If she stops buying coffee it will instead only take her 15 weeks to buy a new laptop

Answer:

8 Hours 15 Minutes

Step-by-step explanation:

12:00 p.m - 3:45 a.m = 8 Hours 15 Minutes

The measure of angle MBT as shown in the diagram is 28 degrees.

An angle is formed from the intersection of two or more lines. Types of angles are obtuse, acute and right angled.

From the diagram:

∠MBN = ∠MBT

17x - 6 = 5x + 18

x = 2

∠MBT = 5(2) + 18 = 28 degrees

The measure of angle MBT as shown in the diagram is 28 degrees.

Find out more on angle at: https://brainly.com/question/25770607

Answer:

B. The function f(x) = tan(x) is an odd function because f(-x) = -f(x)

Step-by-step explanation:

The function f(x) = tan(x) is odd as  [tex]f(-x) = -f(x)[/tex]  so we can conclude the statement B. The function f(x) = tan(x) is an odd function because [tex]f(-x) = -f(x)[/tex] is the true option.

The function is a relation used to determine a value f(x) for a given x using an expression in x.

An even function is when f(x) = f(-x). It is symmetric along the y-axis.

An odd function is when f(-x) = -f(x). It is symmetric along the x-axis.

We are dealing with the function f(x) = tan(x).

We calculate f(-x) = tan(-x) = -tan(x) = -f(x).

∴ The function f(x) = tan(x) is an odd function, and odd functions are symmetric about the origin.

∴ The function f(x) = tan(x) is odd as  [tex]f(-x) = -f(x)[/tex]  so we can conclude the statement B. The function f(x) = tan(x) is an odd function because [tex]f(-x) = -f(x)[/tex] is the true option.

Learn more about odd functions and even functions at

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Answer:

D (-1,-3)

Step-by-step explanation:

If h(x)=-3x-6, plug in for x

-3 =-3(-1)-6

-3=3-6

-3=-3

so two negatives cancel out and get you the positive three minus six, resulting in negative 3, which is also the h(x) value.

Answer:

D

Step-by-step explanation:

Plug it in

Y=3x-6

-3=-3(-1)-6

-3=-3

Answer:

344

Step-by-step explanation:

First we are going to find the area of the top and bottom

8x8=64. Since the top and bottom are the same, we can do 64x2=128.

Now we are going to find the area of the left and right sides.

8x7=54. Since the right and left are the same, we can do 54x2=108.

Now we are going to find the area of the front side and the back side.

8x7=54. Since the front and back are the same, we can do 54x2=108.

Now we add our answers up. 128+108+108=344

Answer:

[tex]=5r^2-17r+5[/tex]

Step-by-step explanation:

[tex]\mathrm{Apply\:rule}:\quad \left(a\right)=a[/tex]

[tex]\left(8r^2-12r+4\right)=8r^2-12r+4[/tex]

[tex]=8r^2-12r+4-\left(3r^2+5r-1\right)[/tex]

[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b[/tex]

[tex]-\left(3r^2+5r-1\right)=-3r^2-5r+1[/tex]

[tex]=8r^2-12r+4-3r^2-5r+1[/tex]

[tex]\mathrm{Group\:like\:terms}[/tex]

[tex]=8r^2-3r^2-12r-5r+4+1[/tex]

[tex]\mathrm{Add\:the\:numbers:}\:4+1=5[/tex]

[tex]=8r^2-3r^2-12r-5r+5[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:8r^2-3r^2=5r^2[/tex]

[tex]=5r^2-12r-5r+5[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:-12r-5r=-17r[/tex]

[tex]=5r^2-17r+5[/tex]

Answer:

2 is not the same as 4.

[tex]2^2[/tex] is the same as 4, since 2*2 = 4.

2 is not the same as 4 but 2x2 is the same as 4

Answer: 70 animals

Step-by-step explanation:

Since Marshall predicted that if 100 cats entered the shelter, 80 of the cats would have already been vaccinated . This means that 80/100 = 4/5 of the animals that enter the shelter are vaccinated.

Let the animals that enter in July be y. This will be:

4/5 × y = 56

0.8y = 56

y = 56/0.8

y = 70

70 animals entered in July

Answer:

not a right triangle in maths

Step-by-step explanation:

FALSE, the Pythagorean Theorem is not satisfied

but true in real life, i mean the shape

Answer:

50+25n=$125 and 3 hours

Step-by-step explanation:

Answer:

[tex]y=-5x+0[/tex]

Step-by-step explanation:

We know that slope intercept form is:

[tex]y=mx+b[/tex]

And our slope is -5, and the variable we use for slope is m:

[tex]m=-5[/tex]

Our new equation becomes:

[tex]y=-5x+???[/tex]

And our y-intercept is 0, and the letter we use to express our y-intercept is b:

[tex]b=0[/tex]

Our new equation is:

[tex]y=-5x+0[/tex]

Hence, the correct answer is [tex]y=-5x+0[/tex]

The expected number of defective bolts are obtained as 175. The correct option is (C).

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

The total number of bolts tested are 24.

And, the number of defective bolts are 5.

Then, the probability of defective bolts is given as,

P(defective bolts) = 5/24

Now, the expected number of bolts can be found as,

Expected number = P(defective bolts) × Total number of bolts tested

⇒ 5/24 × 850 = 175

Hence, the expected number of bolts that will be defective is given as 175.

To know more about probability click on,

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Answer:

14

Step-by-step explanation:

let the number be y

if y is tripled we get 3y

3y = 28 + y

3y - y = 28

2y = 28

y = 14

Answer:

14

Step-by-step explanation:

Let the number be x.

Base on the given

↓ Equation ↓

3x=x+28

Solve:

3 x - x = 28

2 x = 28

x = 28/2

x = 14

Thus, The number is 14.

[RevyBreeze]

7.09 meters

Step-by-step explanation:

first start by using sin of 47 to find the hypotenus.

Then after finding the hypotenus you just have to use cos of 47 to find BC

Answer:

7.09 m

Step-by-step explanation:

Answer:

153.098

153.408

When we look at these numbers, we want to see which one has the greatest digit.

Shown below, I'm going to compare both numbers and start from the hundreds place and gradually go further into the other digits until we've seen which number is the greatest.

153.098:

1

153.408:

1

153.098:

15

153.408:

15

153.098:

153

153.408

153

153.098:

153.0

153.408

153.4

Now, we can automatically know that 153.408 is the greatest because the 4 in the tenths place is bigger than 0 in the tenths place in the other number.

So 153.408 > 153.098, D is your answer.

Answer:

Step-by-step explanation:

Square with side (s) = 3

P = 4s        

s = 3

P = 4*3

P = 12

Square with side (s) = 6

P = 4s

s = 6

P = 4 * 6

P = 24

Answer

It is asking for the ratio of P(with side = 3)/ to P(with side = 6)

So the perimeter ratio is 1/2

The side ratio is 1/2

They are the same.

Answer:

41200 in scientific notation = 4,1 . 10⁴

Answer:

The exponent is 4

[tex]4.12[/tex] × [tex]10^{4}[/tex]

Step-by-step explanation:

Hope this helps

Answer:

Equation of the best fit line is given as  y = - 0.76x + 26.04  Now we need to find the decrease in time spent in doing homework for increase in one hour in time spent in watching TV.

Step-by-step explanation:

hope this helps

have an awesome day -TJ

Answer: 21

3(4) + 2(5) - 1 = 21