Hi people! Can you help me figure this out? I'll mark brainliest!

Answer:

23.1 years  (nearest tenth)

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 1200=600\left(1+\dfrac{0.03}{12}\right)^{12t}[/tex]

[tex]\implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf 2=\left(1.0025\right)^{12t}[/tex]

Take natural logs:

[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]

[tex]\implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]

[tex]\implies t=23.13377513...[/tex]

[tex]\implies t=23.1\: \sf years \:\:(nearest\:tenth)[/tex]

The money will double in value in approximately [tex]\boxed{\sf 23.1}[/tex] years.

Used formula

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

[tex]\\ \implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf 2=\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]

[tex]\\ \implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]

[tex]\\ \implies t=23.1years[/tex]

the elegante is aborto 3

If we want the slope to be -6/7, then the value of x must be -5.

Remember that if a linear equation passes through (x₁, y₁) and (x₂, y₂), then the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we have the points (x, 9) and (9, -3), and the slope must be -6/7, so we need to solve:

[tex]\frac{- 3 - 9}{9 - x} = \frac{-6}{7} \\\\\frac{-12}{9 - x} = \frac{-12}{14}[/tex]

Where on the second line we multiplied and divided the right fraction by 2.

Comparing the fractions, we see that we must have:

9 -x = 14

9 - 14 = x

-5 = x

So the value of x must be -5.

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Answer:

C

Step-by-step explanation:

a = 4

b = 5

c = 2

C = arccos((a² + b² - c²) / 2ab)

C = arccos((16 + 25 - 4) / 2(4)(5))

C = arccos(37 / 40)

C = 22.33°

2abcosC

2(4)(5)cos(22.33)

40(0.925)

37

Option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have from law of cosines that a² + b² - 2abcosC = c²

We have to find the value of 2abcosC.

Now let us find the value of C

C = arccos((a² + b² - c²) / 2ab)

C = arccos((16 + 25 - 4) / 2(4)(5))

C = arccos(37 / 40)

C = 22.33°

Now plug in the value of C in  2abcosC.

2abcosC

=2(4)(5)cos(22.33)

=40(0.925)

=37

Hence, option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.

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The water level increases by 0.608 meters per minute when the water is 3.5 m deep

The given parameters are:

The relationship between the radius and height is:

r/h = 3/7

Make r the subject

r = 3h/7

The volume of a cone is;

[tex]V = \frac 13\pi r^2h[/tex]

This gives

[tex]V = \frac 13\pi (\frac{3h}{7})^2h[/tex]

Expand

[tex]V = \frac{3h^3}{49}\pi[/tex]

Differentiate

[tex]V' = \frac{9h^2}{49}\pi h'[/tex]

Make h' the subject

[tex]h' = \frac{49}{9\pi h^2}V'[/tex]

When the water level is 3.5.

We have:

[tex]h' = \frac{49}{9\pi * 3.5^2}V'[/tex]

Also, we have:

V' = 4.3

So, the equation becomes

[tex]h' = \frac{49}{9\pi * 3.5^2} * 4.3[/tex]

Evaluate the products

[tex]h' = \frac{210.7}{346.36}[/tex]

Evaluate the quotient

h' = 0.608

Hence, the water level increases by 0.608 meters per minute

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Answer: C, 5, 5√3

Step-by-step explanation:

The short leg of a 30-60-90 triangle equal half the hypotenuse, 10/2 = 5. The long leg equals √3 times the short leg, 5*√3 = 5√3.

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Answer:

35.1% chance of going sledding

Step-by-step explanation:

45% chance of snow on Friday

Convert percentage to decimal form (divide by 100)

45% = 0.45

78% chance of sledding if it snows

Convert percentage to decimal form (divide by 100) to multiply

78% = 0.78

Multiply to find the probability of both occurring

0.78 * 0.45 = 0.351

Convert back into a percentage (multiply by 100)

0.351 = 35.1% chance of sledding

Let me know if you have any questions!

Step-by-step explanation:

please mark me as brainlest

Step-by-step explanation:

108 = 60%

1% = 60%/60 = 108/60 = 1.8

100% = 1%×100 = 1.8×100 = 180

how many do not study French ?

the remainder of the students. that is 40% (100% - 60%) or 72 students (40×1.8 or simply 180-108).

Answer:

72 students do not study French.

Step-by-step explanation:

60% = 108 students

1. 108 ÷ 60 = 1.8 ( this is to find 1% of the students)

2. 1.8(1%) × 40 = 72

To check the answer:

108 + 72 = 180

180 × 60% = 108

Answer:

[tex]A) \ x=-1 \ ^ +_-\frac{\sqrt{13} }{\sqrt{6}}.[/tex]

Step-by-step explanation:

if to solve the given equation, then

D=6²+42=78;

[tex]\left[\begin{array}{ccc}x=\frac{-6-\sqrt{78}}{6} \\x=\frac{-6+\sqrt{78}}{6} \end{array} \ = > \ \left[\begin{array}{ccc}x=-1-\sqrt{\frac{13}{6} } \\x=-1+\sqrt{\frac{13}{6} } \end{array}[/tex]

Answer:

Well, it depends if you are asking the rate per gallon it would be 12 miles per gallon.

Answer:576

Step-by-step explanation:

24 squared is 576

After 85 minutes of calls, there are $27.25 left on the card.

A linear equation in slope-intercept form is:

y = a*x + b

Where a is the slope.

If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, we know that the line passes through the points (22, 36.7) and (52, 32,20)

(points of the form (time, dollars)).

So the slope is:

[tex]a = \frac{32.2 - 36.7}{52 -22} = -0.15[/tex]

The linear equation is then:

y = -0.15*x + b

To find the value of b, we use the point (22. 36.7)

36.7 = -0.15*22 + b

36.7 + 0.15*22 = b = 40

Then the linear equation is:

y = -0.15*x +40

The amount remaining in the credit card after 85 minutes is given by evaluating the above equation in x = 85.

y = -0.15*85 + 40 = 27.25

This means that after 85 minutes of calls, there are $27.25 left on the card.

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Answer:

option N is the correct option, apply Formula of area of rectangle and triangle by splitting figure into 2 parts

Answer:

There isn't a photo

Step-by-step explanation:

There is no photo

The  probability that more than 562 drivers is 0.9328

It is a branch of mathematics that deals with the occurrence of a random event.

Given: p = 0.60

n = 900

Let X denote the number of drivers that wear a seat belt,

P(X > 562)

[tex]\mu[/tex] = n*p = 900(0.60) = 540

[tex]\sigma^{2}[/tex]= n*p*(1-p)

=900*0.60*0.40

=216

P(X >562) = Pr( Z > 1.4976)

                = 0.9328

Hence, the probability that more than 562 drivers is 0.9328

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The simplified form of the expression 2/5 x (-7)x 5/2 would be -7.

When two fractions are multiplying each other, the numerator of both fractions multiplies each other, likewise the denominator of both fractions respectively.

Use the property of real numbers to write the expression

[tex]\dfrac{2}{5} \times (-7) \times \dfrac{ 5}{2}\\\\\dfrac{10}{10} \times (-7) \\\\-7 \times 1\\\\= -7[/tex]

Therefore, The simplified form of the expression would be -7.

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Answer:

h=-2

Step-by-step explanation:

the graph was shifted 2 units left

The alloy of copper will be 600 ounces.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Let us represent

Number of ounce of 30% copper = x

Hence, our Equation will be given below:-

x × 30% + 200 × 70% = (x + 200) × 40%

0.3x + 140 = (x + 200)0.4

0.3x + 140 = 0.4x + 80

Collect like terms

0.4x - 0.3x = 140 - 80

0.1x = 60

x = 60/0.1

x = 600 ounces

Therefore the alloy of copper will be 600 ounces.

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

Explanation:

The white rectangle is 3 by 6 with area of 3*6 = 18 square inches.

The larger rectangle is 8 by 5 with area of 8*5 = 40 square inches.

The difference of these will get us the shaded area:

40 - 18 = 22 square inches

Answer:

-4

Step-by-step explanation:

The equation for slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

m: Slope

(6, 2) = [tex](x_1, y_1)[/tex]

(4, 10) = [tex](x_2, y_2)[/tex]

Substitute these values into the equation:

[tex]m=\frac{10-2}{4-6}=\frac{8}{-2}=-4[/tex]

Therefore the slope is -4.

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the slope of the line that passes through the points? 2 points given

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The formula used here, is [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{\dfrac{10-2}{4-6}}[/tex] | subtract

[tex]\bf{\dfrac{8}{-2}}[/tex] | evaluate

[tex]\bf{-4}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

           [tex]\bf{=Slope\;-4}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Answer:

x≥11

Step-by-step explanation:

4x-3≥41

4x≥41+3   -44

x≥44/4 = 11

Answer:

y = -2x + 64

Explanation:

The x represents the time in minutes and y represents distance in km.

Determine coordinates: (0, 64), (17, 30)

Find slope:

[tex]\sf slope : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) : \dfrac{30-64}{17-0} = -2[/tex]

Find equation:

[tex]\sf y- y_1 = m(x - x_1)[/tex]

[tex]\sf y - 64 = -2(x - 0)[/tex]

[tex]\sf y = -2x + 64[/tex]

The graph is attached with the answer, This is looking like a horizontal staircase

A step function is a piece wise function whose all pieces are horizontal line or a point.

It is given in the question to graph the interval

-2 ≤x≤2

for f(x) = |x+3|

-2    1

-1     2

0     3

1      4

2     5

The graph is attached with the answer.

This is looking like a horizontal staircase

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Answer:

70.445

Step-by-step explanation:

you have to subtract 36.5 by 193.

Answer: [tex]\frac{1}{7^{2}}[/tex]

Step-by-step explanation:

Using the exponent rule [tex]a^{b} \cdot a^{c}=a^{b+c}[/tex], we get that

[tex]7^{3} \cdot 7^{-5}=7^{-2}[/tex]

Then, using the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex], we get that

[tex]7^{-2}=\boxed{\frac{1}{7^{2}}}[/tex]

Answer:

First Inverse function= f^-1(x)=x/3-5/3

Second Inverse function=f^-1(x)=x/3-5/3

Step-by-step explanation:

Answer:

1282kg

Step-by-step explanation:

1.0*1.12*1.1=1.232 tonnes

50kg + 1232kg = 1282kg

Hope this helps :)