Use the Cross Products Property to solve the proportion
5/n =16/32

Answer:

She saved $48; She had $72 remaining

Step-by-step explanation: She started off with $120. 20% of $120= $24, 25% of $96= $24. $24 + $24= $48.  $120(total) - $48(total money saved) = $72(money left).

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The amount of money left is $72

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Amount = $120

Amount spend on food.

= 20% of 120

= 20/100 x 120

= $24

Amount remaining.

= 120 - 24

= $96

Amount spend on clothes.

= 25% of 96

= 1/4 x 96

= $24

Amount remaining.

= 96 - 24

= $72

Thus,

The amount of money left is $72

Learn more about percentages here:

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Answer:

CD = 2 units

Step-by-step explanation:

in the given right triangle ΔCDE,

By applying tangent rule,

tan(∠E) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

            = [tex]\frac{\text{CD}}{\text{DE}}[/tex]

tan(30)° = [tex]\frac{\text{CD}}{2\sqrt{3}}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{\text{CD}}{2\sqrt{3}}[/tex]

CD = [tex]\frac{2\sqrt{3}}{\sqrt{3}}[/tex]

CD = 2 units

Therefore, CD = 2 unit will be the answer.

Answer:

942.5 in²  

Step-by-step explanation:

The formula for the area (A) of a sector of a circle is

A = ½r²θ

where θ is the angle in radians.

1. Convert the angle to radians

θ = 125°  

[tex]\theta = 125^{\circ} \times \dfrac{\pi \text{ rad }}{180^{\circ}} =\frac{25}{36} \pi\text{ rad}[/tex]

2. Area swept out by wiper arm

A = ½r²θ = ½ × (30 in)² × θ = ½ × 900 in²× θ = 450 θ in²

3. Area missed by wiper

A = ½r²θ = ½ × (6 in)² × θ = ½ × 36 in²× θ = 18 θ in ²

4. Area covered by wiper

A = 450 θ in² - 18 θ in² = 432 θ in²

5. Insert the value of θ

A = 432 × 25/36 π in² = 300π in² ≈ 942.5 in²

The area swept out by the wiper blade is 942.5 in².

Answer:

The number of hours Stephanie will have driven before Tina catches up to her is 2.5 hours

Step-by-step explanation:

Given:

56s=70t

s=t+1/2

Solution

56s=70t

s=t+1/2

Substitute s=t+1/2 into 56s=70t

56s=70t

56(t+1/2)=70t

56t+28=70t

28=70t - 56t

28=14t

Divide both sides by 14

28/14=14t/14

2=t

t=2

Recall,

s=t+1/2

s=2+1/2

=4+1/2

s=5/2

Or

s=2.5 hours

Answer:

work is shown and pictured

Answer:

C

Step-by-step explanation:

Brainliest?

Answer:

Janine=12.6(repeating) Samantha=15.6(repeating) Lucy=19.6(repeating)

Step-by-step explanation:

Lets concentrate on one person, Janine.

Janine = Lucy - 7

Janine = Samantha - 3

If the averae of the 3 people's ages is 16, then we should multiple that by three to get 48, the number of their ages combined.

Janine + Lucy + Samantha = 48

The differences between Janine to Lucy and Janine to Samantha combined is 10, so we can subtract that from 48 to get 38, which is 3 times Janines age.

38/3=12.6(repeating)

That is Janine's age. We can use that to find both Lucy's and Samantha's ages respectively by using their equations. Lucy's is 19.6(repeating) and Samantha's is 15.6(repeating). I hope you can give me brainliest, and that this helped!

Answer:

B -5, and 5

Step-by-step explanation:

you can't have zero on the bottom

Answer:

Below

Step-by-step explanation:

Coterminal angles are angles with same terminal angles

Mathematically speaking these angles should have the same coordinates in a trigonomitrical circle

●●●●●●●●●●●●●●●●●●●●●●●●

Angles like 0° and 360° are coterminal since to we made a spin from 0° to 360°

For two angles A and B to be coterminal they should verify this relation :

A = B + k*360° with k an integer

So A-B = k*360°

●●●●●●●●●●●●●●●●●●●●●●●●

7) :

35° and 395°

395° -35° = 360°

360° is a multiple of 360° so these angles are coterminal

8) :

140° and 860°

860° - 140° = 720°

720° is a multiple of 360°

720 = 360° × 2

9) :

350° and -710°

350 -(-710) = 350+ 710 = 1060°

1060° isn't a multiple of 360°

So these angles aren't coterminal

10) :

130° and -230°

130 -(-230) = 130+230 = 360°

So these angles are coterminal

11) :

30° and -690°

30 -(-690) = 30+ 690 = 720°

720 is a multiple of 360 so these angles are coterminal

12) :

210° and 10°

210-10 = 200

200 isn't a multiple of 360 so these angles aren't coterminal

Answer:

y = - 49

Step-by-step explanation:

Given

7x - 2y = 35 ← substitute x = - 9 into the equation

7(- 9) - 2y = 35, that is

- 63 - 2y = 35 ( add 63 to both sides )

- 2y = 98 ( divide both sides by - 2 )

y = - 49

Answer:

[tex]\boxed{y = -49}[/tex]

Step-by-step explanation:

=> [tex]7x-2y = 25[/tex]

Given that x = -9

=> [tex]7(-9)-2y = 35[/tex]

=> [tex]-63 -2y = 35[/tex]

Adding 63 to both sides

=> [tex]-2y = 35+63[/tex]

=> [tex]-2y = 98[/tex]

Dividing both sides by -2

=> [tex]y = 98/-2[/tex]

=> [tex]y = -49[/tex]

Answer:

x = 1, x = 2

Step-by-step explanation:

Given

f(x) = g(x) - 1, that is

x² - 2x - 1 = x - 1 - 2

x² - 2x - 1 = x - 3 ( subtract x - 3 from both sides )

x² - 3x + 2 = 0 ← in standard form

(x - 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

Answer:

[tex]f^-^{1} (x)=\frac{19}{x}[/tex]

Step-by-step explanation:

To find the inverse of this function, switch the variables like this:

[tex]\frac{19}{x}\\\\x=\frac{19}{y} \\[/tex]

Then, solve for y, like this:

[tex]y= \frac{19}{x} \\[/tex]

Replace y with [tex]f^-^{1} (x)[/tex].

[tex]f^-^{1} (x)=\frac{19}{x}\\[/tex]

Answer:

Step-by-step explanation:

The first thing we are going to do is to fill in the other angles that we need to solve this problem. You could find ALL of them but all of them isn't necessary. So looking at the obtuse angle next to the 35 degree angle...we know that those are supplementary so 180 - 35 = the obtuse angle in the small triangle. 180 - 35 = 145. Within the smaller triangle we have now the 145 and the 10, and since, by the Triangle Angle-Sum Theorem all the angles have to add up to equal 180, then 180 - (10 + 145) = the 3rd angle, so the third angle is 180 - 155 = 25. Now let's get to the problem. If I were you, I'd draw that out like I did to keep track of these angles cuz I'm going to name them by their degree. In order to find d, we need to first find the distance between d and the right angle. We'll call that x. The reference angle is 35, the side opposite that angle is 12 and the side we are looking for, x, is adjacent to that angle. So we will use the tan ratio to find x:

[tex]tan(35)=\frac{12}{x}[/tex] Isolating x:

[tex]x=\frac{12}{tan(35)}[/tex] so

x = 17.1377 m

Now we have everything we need to find d. We will use 25 degrees as our reference angle, and the side opposite it is 12 and the side adjacent to it is

d + 17.1377, so that is the tan ratio as well:

[tex]tan(25)=\frac{12}{d+17.1377}[/tex] and simplifying a bit:

[tex]d+17.1377=\frac{12}{tan(25)}[/tex] and a bit more:

d + 17.1377 = 25.73408 so

d = 8.59, rounded

Answer:

16

Step-by-step explanation:

Subtracting the given expressions, that is

3b² - 8 - (b(b² + b - 7) ) ← simplify parenthesis

= 3b² - 8 - (b³ + b² - 7b) ← distribute parenthesis by - 1

= 3b² - 8 - b³ - b² + 7b ← collect like terms

= - b³ + 2b² + 7b - 8 ← substitute b = - 3

= - (- 3)³ + 2(- 3)² + 7(- 3) - 8

= - (- 27) + 2(9) - 21 - 8

= 27 + 18 - 21 - 8

= 16

Answer:

y=-4x-3

Step-by-step explanation:

y=mx+b

y=b=-3 ( y intercept is when x=0, then y=b=-3)

y=-4x-3

Each tick on the graph represents a single unit.

Thus, counting the ticks, we see that the graph starts at x=2. We also see that the graph ends at x=5.

Thus, the domain is [tex]2 \leq x \leq 5[/tex]

Let me know if you need any clarifications, thanks!

Answer:

D

Step-by-step explanation:

Find the x intercepts from the equation and apply them to the graphs. It matches up with D. Your thought is correct

Answer:

[tex]\boxed{\mathrm{D}}[/tex]

Step-by-step explanation:

[tex]y= (x + 1)(x - 1)(x - 4)[/tex]

Let x = 0, find the y-intercept.

[tex]y= (0 + 1)(0 - 1)(0 - 4)[/tex]

[tex]y= ( 1)(- 1)(- 4)[/tex]

[tex]y=4[/tex]

The function crosses the y-axis at 4.

The only graph that shows this is graph D.

Round this however you need to.

===========================

Work Shown:

Check out the diagram below. We have the following points

Based on those points, we know that

Which allows us to find the distance from C to D. Focus solely on triangle EDC. Use the sine ratio to find x.

sin(angle) = opposite/hypotenuse

sin(angle EDC) = CE/CD

sin(56) = 7130/x

x*sin(56) = 7130

x = 7130/sin(56)

x = 8600.33397283284 approximately

Make sure your calculator is in degree mode.

Answer:

x = 1/(3k)

Step-by-step explanation:

30kx-6kx=8

Combine like terms

24 kx = 8

Divide each side by 24k

24kx / 24k = 8/(24k)

x = 1/(3k)

Answer:

4 hours 21 minutes 17 seconds.

Step-by-step explanation:

1km = 6 minutes

42.195km = ?

42.195 × 6 = 253 minutes 17 seconds = 4 hours 21 minutes 17 seconds.

Answer:

4 hours 21 minutes 17 seconds.

Step-by-step explanation:

Complete Question:

Convert 3x-y+2=0 in rectangle form to polar form

Answer:

r ( 3cosθ - sinθ) = -2

Step-by-step explanation:

The equation so given is already in rectangular form, the task is to convert it to polar form.

3x - y + 2 = 0

To transform an equation from the rectangular to the polar coordinate:

x = r cosθ

y = r sinθ

Substitute the representations for x and y into the given equation:

3(r cosθ) - (r sinθ) + 2 = 0

3rcosθ - rsinθ = -2

The polar representation of the equation then becomes:

r ( 3cosθ - sinθ) = -2

Answer:

z(0.05) = -1.645

Step-by-step explanation:

z(0.05) = -1.645  is the left tail of the normal probability curve with 5% of the area under the curve.

Answer:1.645

Step-by-step explanation:

Answer:

Step-by-step explanation:

If a scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour and the function y = 35 ∙ 3x models the number of bacteria after x hours, in order to estimate when there will be about 550 bacteria in the culture we will substitute y = 550 into the modeled equation and calculate the value of x as shown;

If y = 35*3x

when y = 550

550 = 35*3x

Dividing both sides by 35;

550/35 = 35*3x/35

3x = 550/35

x = 550/3*35

x = 550/105

x = 5.24

This means that there will be 550 bacteria in the culture after approximately 5 hours

Answer:

$200 at 2%.

$2200 at 3.5%.

Step-by-step explanation:

Let the two amounts be x and y.

x earns 2% interest, and y earns 3.5% interest.

Since the total is $2400, then

x + y = 2400

Now we can solve for y and express the second amount in terms of x.

y = 2400 - y

The two amounts are x and 2400 - x.

In one interest period, the amount of interest earned is the amount of money in the account multiplied by the interest.

2% = 0.02; 3.5% = 0.035

The x amount earns 0.02x interest.

The y amount earns 0.035y interest.

The total interest earned is the sum of the interest amounts of the two accounts.

0.02x + 0.035y

We now replace y with 2400 - x, and we set the sum of the interest amounts equal to the total interest earned, $81.

0.02x + 0.035(2400 - x) = 81

The equation above is the linear equation.

Now we solve it. Distribute on the left side.

0.02x + 84 - 0.035x = 81

Combine like terms on the left side.

-0.015x + 84 = 81

Subtract 84 from both sides.

-0.015x = -3

Divide both side by -0.015.

x = 200

$200 was deposited in the account earning 2%.

y = 2400 - x

y = 2400 - 200

y = 2200

$2200 was deposited in the account earning 3.5%.

Answer:

Step-by-step explanation:

The inscribed angle intersects an arc that is half the measure of the of the arc intersected by the central angle. The inscribed angle's arc measures 36%, and the central angle's arc measure 72%

Answer:

75

%Step-by-step explanation:

The inscribed angle intersects an arc that is half the measure of the of the arc intersected by the central angle.

Answer:

Ok, I can see only a) to c)

a) Lucy spent the most time reading.

b) 20 minutes.

c) 22 minutes.

Step-by-step explanation:

Reason for b):

First convert hours to minutes.

1 hour = 60 minutes

4 hours = ?

4 × 60 = 240 minutes.

Homework is 30°

Total in the pie chart is 360° so:

30/360 × 240 mins = 20 mins

Answer is Zac spent 20 minutes to do his homework.

Reason for c):

Watching TV:

Zac: 135°

Lucy: 102°

Zac:

135/360 × 240 minutes = 90 minutes

Lucy:

102/360 × 240 minutes = 68 minutes

To find how many minutes Zac spent watching TV than Lucy:

90 minutes - 68 minutes = 22 minutes.

Do you understand, Kiara 12004?

Answer:

  One of the other perpendicular bisectors must pass through point B

Step-by-step explanation:

Let's look at the choices:

 — incenter equidistant from B and C.

The incenter is on the perpendicular bisector of BC. Every point on that line is equidistant from B and C. This statement is True.

__

 — angles B and C are congruent.

As we said above, A (on the perpendicular bisector of BC) is equidistant from B and C. That makes the triangle isosceles. The congruent angles are B and C, opposite congruent sides AC and AB. This statement is True.

__

 — the perpendicular bisector of BC passes through the incenter.

The incenter is the point of concurrence of the angle bisectors. Since the perpendicular bisector of BC goes through the a.pex of triangle ABC at A, it is the angle bisector there. Hence the incenter lies on that line. The statement is True.

__

 — B lies on one of the other perpendicular bisectors.

This will be true if the triangle is equilateral. Nothing in the problem statement indicates this is the case. The statement is False.

This question is incomplete because the options are missing; here is the missing section:

A respondent is randomly selected among those who believe that penguins are threatened  "a great deal." Approximately what is the probability that this respondent will be female?​

A. 29%

B. 38%

C. 53%

D. 62%

The correct answer to this question is D. 62%

Explanation:

The general formula to calculate the probability of one simple event is to divide the number of outcomes that will lead to the specific event, by the number of total outcomes. In the case presented, we know the total of people who answered penguins are threatened "a great deal" is 323, which represents the total of outcomes. Additionally, as we need to find out the probability of a respondent in this category is a female, the number of ways this specific event can happen is 200 (total number of female respondents).

This means the probability is equal to 200 (number of female respondents) / 323 (total respondents) which is equivalent to 0.619 or 0.62 if the number is rounded. Additionally, this probability can be expressed as a percentage by multiplying this by 100, which means the probability is 62%.

Answer:

5√26/13

Step-by-step explanation:

5√2/√13 multiply the nominator and denominator by √13 to rationalize the denominator

5√2√13/√13√13 ( √13×√13=13)

5√26/13

there is answer in multiple choice but this is the correct one

Step-by-step explanation:

sorry I can only explain as there are no labels to each diagram

The first diagram is single and can solved using triangular formular given as 1/2 ×base × height

A = 1/2 × 5 × 12

A = 30cm^2..

as for the second one...it consist of 2 diagrams which will be solved separately before adding ...it can simply be done using Pythagoras theorem..

To get the smaller part ...out tita is 45degrees while our adjacent is 4 and opposite is x we are to find x which is the height...

using SOH CAH TOA...

WE HAVE TAN45= opp/adj

Tan45= x/ 4

Tan 45 =1 ...so

1 = x/ 4

and x= 4 ...

so...having our height as 4 and base as 4 ..

Area of smaller triangle become 1/2 × 4 × 4

A = 8cm^2 ...

......SOLVING FOR THE SECOND DIAGRAM ..

WE HAVE the height as ( dotted spot + undotted spot ) = 4 + 4 = 8cm

and our base can be gotten from

Tan45 = opp / adj

1 = 8/x ..

x = 8cm ....so the base is 8 and the height is 8

..

The Area becomes 1/2 × 8×8 = 32cm ...

Total area becomes 32cm + 8cm = 40cm^2

Answer:

86.55 ft

Step-by-step explanation:

First find the perimeter for 3 sides of the rectangle that are solid

24+15+24 = 63

The we find the circumference for 1/2 of the circle

C = pi d

The diameter is 15 and pi = 3.14

But we only want 1/2

1/2 C = 1/2 pi d

        = 1/2 ( 3.14) * 15

       =23.55

Add the lengths together

23.55+63 =86.55 ft