Can someone give me the steps to solving this?

Answer: x = log₃₇(12)

Step - by - step explanation:

1. Remove the variable from the exponent using logarithms

37^x=12

Take the common logarithm of both sides of the equation:

log₁₀(37^x)=log₁₀12)

Use the log rule:  log_a(x^y)=y*log_a(x) to move the exponent outside the logarithm:

x*log₁₀(37)=log₁₀(12)

2. Isolate the x-variable

x*log₁₀(37)=log₁₀(12)

Divide both sides of the equation log₁₀(37) by:

x = log₁₀(12) / log₁₀(37)

Use the formula  [tex]log_{b}(x)/log_{b}(a) = log_{a} (x)[/tex]

to combine the logarithms into one:

x=log₃₇(12)

Decimal form:

x=0.6881648129099501

Hope this helps!

Answer:

2x^3 - 3x^2 + 7x - 3

Step-by-step explanation:

Area = length * width

= (2x - 1)(x^2 - x + 3)

= 2x(x^2 - x + 3) - 1(x^2 - x + 3)

= 2x^3 - 2x^2 + 6x - x^2 + x - 3

= 2x^3 - 3x^2 + 7x - 3

Answer:

6.5

Step-by-step explanation:

Median is always the middle number of the set of data, so lets re order the numbers least to greatest

1,2,4,5,6,7,8,8,9,12

Since there's an even amount there wont be an exact middle number, however we know its in-between 6 and 7. So we can do 6+7 = 13 and then 13/2 = 6.5 to get the middle number or median.

Answer:

30.34 degree

Step-by-step explanation:

Apply sine formula

[tex]\frac{sin\left(A\right)}{a}=\frac{sin\left(B\right)}{b}[/tex]

[tex]\frac{\sin \left(45^{\circ \:}\right)}{7}=\frac{\sin \left(b\right)}{5}[/tex]

->simplify

[tex]\frac{\sin \left(b\right)}{5}=\frac{\frac{\sqrt{2}}{2}}{7}[/tex]

you will get

[tex]\sin \left(b\right)=\frac{5\sqrt{2}}{14}[/tex]

which
sin b is about 0.50507

[tex]sin^{-1}\left(0.50507\right)[/tex]

->arc sine in degree mode

the answer is 30.34

The wrong conclusions that can be drawn from the circle graph are:

The Country section has the smallest area.

The Classical section is not included in the Circle Graph.

A circle graph is a graph that displays information in a circle. The circle is divided into slices which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees

In the circle graph, the country section has a percentage of 10% while the classical section has a percentage of 2%.

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Answer:

the answer is D  

Step-by-step explanation:

look at the table there are 5 music genres but there's only 4 on the circle graph.

assuming is simple interest

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$960\\ P=\textit{original amount deposited}\dotfill & \$3840\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 960 = (3840)(0.05)(t)\implies \cfrac{960}{(3840)(0.05)}=t\implies 5=t[/tex]

Answer:

x = 200

Step-by-step explanation:

Given equation:

[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30[/tex]

Steps:

1. Substitute 15 as the value of y in the equation:

[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\Rightarrow \dfrac{1}{5}x-\dfrac{30}{3}=30\ \textsf{[ simplify ]}\\\\\Rightarrow \dfrac{1}{5}x-10=30[/tex]

2. Add 10 to both sides:

[tex]\sf \dfrac{1}{5}x-10+10=30+10\\\\\Rightarrow \dfrac{1}{5}x=40[/tex]

3. Multiply both sides by 5 to isolate x:

[tex]\sf 5\left(\dfrac{1}{5}\right)x=5(40)\\\\\Rightarrow x=200[/tex]

4. Check your work:

[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30\ \textsf{[ substitute 200 for x, and 15 for y ]}\\\\\dfrac{1}{5}(200)-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\dfrac{200}{5}-\dfrac{30}{3}=30\ \textsf{[ divide ]}\\\\40-10=30\ \textsf{[ subtract ]}\\\\30=30\ \checkmark[/tex]

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Hey there!

[tex] \boxed{\bold{\green{ x = 200}}} [/tex]

[tex] \\ [/tex]

Given expression :

[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{y} = 30 } [/tex]

1) Substitue 15 for [tex] \sf{\orange{y}} [/tex] :

[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{ \times 15} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - \frac{30}{3} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]

[tex] \\ [/tex]

2) Solve for x :

[tex]\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]

⇢Add 10 to both sides of the equation :

[tex]\sf{ \frac{1}{5} \green{x} - 10 \: \bold{+ \: 10}= 30 \: \bold{+ \: 10 }} \\ \\ \implies \sf{\frac{1}{5} \green{x} \: = 40 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

⇢Multiply both sides of the equation by 5:

[tex] \Big( \dfrac{1}{5} \green{x}\Big) \: \bold{ \times \: 5}=40 \: \bold{ \times \: 5} \\ \\ \implies \sf{\dfrac{5}{5} \green{x} \: = 200} \\ \\ \implies \green{ \boxed{\sf{x = 200}}}[/tex]

[tex] \\ [/tex]

3) Let's check our answer by replacing [tex] \green{x} [/tex] with 200 and [tex] \orange{y} [/tex] with 15 :

[tex] \sf{\dfrac{1}{5}\overbrace{\green{\times \: 200}}^{\green{x}} - \dfrac{2}{3}\underbrace{\orange{\times \:15}}_{\orange{y}}= \dfrac{200}{5} - \dfrac{30}{30} = 40 - 10 = \boxed{ 30} } [/tex]

[tex] \\ \\ [/tex]

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Answer:

Radius=4 units

Centre= (0,-10)

Step-by-step explanation:

Given equation of circle is x^2 +(y-10)^2=16

Comparing it with (x-h)^2 +(y-k)^2 = r^2 ,we get,

r=4

Since, centre of a circle=(h,k)=(0,-10)

Answer:

Center (0;10) Radius= 4. Make me brainliest? :(

Step-by-step explanation:

[tex](x + 0)^{2} + (y - 10)^{2} = 16 \\ center(0.10) \\ radius = \sqrt{16} = 4[/tex]

Answer:

132°

Step-by-step explanation:

We use the circle theorem which states that :

Opposite angles in a cyclic quadrilateral add up to 180 .

Now we know that angles ADC and ABC add up to 180. So :

We make an equation and solve for x :

x+(3x-12) = 180

4x-12 = 180

4x = 192

x = 48

Now we substitute the value of x into Angle B :

3(48) -12 =

144 - 12 = 132

Angle B = 132 °

Hope this helped and have a good day

The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth if  you have $1000 and need to buy 10 chairs worth $5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that you have $1000 and need to buy 10 chairs worth $5. Let x represent the money that can be spent on the booth, hence:

x + 10(5) ≤ 1000

The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth, if you have $1000 and need to buy 10 chairs worth $5.

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The shortest height of the box that will hold the map is 6 ft option (C) is correct.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

We have:

Dina is shipping a wall map to a collector. When the map is rolled up, it measures.

From the figure we can apply the Pythagoras theorem to find the length BA:

BA² = 3² + 3²

BA = √18

Again applying Pythagoras theorem:

The height

AD² = 7² - (√18)²

AD² = 31

AD = √31 ft = 5.56 ft ≈ 6 ft

Thus, the shortest height of the box that will hold the map is 6 ft option (C) is correct.

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Answer:

The answer is (0.5, 0)

Step-by-step explanation:

1. 20,000×10%=2,000

2. 20,000×14%=2,800

3. 20,000×5%=1,000

4. Business Marketing

5. 20,000×30%=6,000

Answer:

the answer is in picture

Step-by-step explanation:

hope it will help you

By taking a quotient between the number of packages and the rate at which James works, we conclude that he will need 467 hours.

We know that James wraps at a rate of 8 packages in one hour. Then to get the time in which he can wrap a number N of packages, we need to take the quotient between N and 8.

In this case, N = 3,736.

Taking the quotient we get:

3,736/8 = 467

This means that in 467 hours he will wrap the 3,736 packages.

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The valid solution for the positive demand is (6,3)

The equation of the function is given as:

[tex]C(t) = -\sqrt{t^2 - 4t - 12} + 3[/tex]

Next, we test the options::

Option (a): (t, C(t)) = (2,3)

This gives

[tex]-\sqrt{2^2 - 4*2 - 12} + 3 = 3[/tex]

Evaluate the radicand

[tex]-\sqrt{-16} + 3 = 3[/tex] ---- this is not true (square root of -16 is a complex number)

Option (b): (t, C(t)) = (6,3)

This gives

[tex]-\sqrt{6^2 - 4*6 - 12} + 3 = 3[/tex]

Evaluate the radicand

[tex]-\sqrt{0} + 3 = 3[/tex]

Evaluate the root

0 + 3 = 3

Evaluate the sum

3 = 3 ---- this is true

Hence, the valid solution for the positive demand is (6,3)

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Using a calculator, it is found that the equation of linear regression that fits the data is given by:

C. y=-0.295x+20.667

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points are given as follows: (1, 20.71), (2, 19.69), (3, 19.61), (4, 19.64), (5, 19.26). Hence the equation is:

Doing this, the equation is:

y = -0.295x + 20.667.

Hence option C is correct.

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Answer:

h=8.0

Step-by-step explanation:

law of sines

sinA/a=sinB/b

b/a=sinB/sinA

b = a times sinB/sinA

b = 10 times sin53/sin90

on a calculator type sin53 in degrees

b = 10 times 0.7986/1

b = 7.986

The correct true statement is: b.  The swimmer comes back up 9 seconds after the timer was started.

Given:

h(t)=t^2−12t+27

Let velocity of the function= 0

h(t) = 2t - 12

0 = 2t - 12

2t = 12

Divide both side by 2t

t=12/2

t = 6secs

Substitution

h(6) = 6²-12(6)+27

h(6) = 36 - 72 + 27

h(6) = -36 + 27

h(6) = -9 feet

The correct statement is b.

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Answer:

Option A: Linear Regression

Step-by-step explanation:

The sale values do not increase in a quadratic or exponential function.

The area of the rectangle is 64.8 square .inch

A rectangle is a polygon with four sides , opposite sides are parallel and equal.

It is given that

A rectangle is divided into exactly 20 congruent squares

If they are lined up the Length is 36 inches

Therefore the length of each square or the side of the square = 36/20

= 1.8 inch

The area of the rectangle will be

20* Side of square * Side of square

=20*1.8*1.8

= 64.8 square inch

The area of the rectangle is 64.8 square .inch

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Answer:

-1

Step-by-step explanation:

Let the points be (0, a) and (a, 0) (As it mentions the intercepts are equal)

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

Applying slope formula :

⇒ m = 0 - a / a - 0

⇒ m = -a/a

⇒ m = -1

Answer:

Rational numbers is a ratio (i.e., P/Q and Q≠0)

Irrational numbers cannot be expressed as a fraction.

so a

Rational numbers can show a Fraction

Irrational numbers can not show a Fraction

Hope This Helped

Answer:

Rational numbers are any infinite number or ratio that goes on and on and represents such mathematical values, e.g five-over-twelve is a rational number because it is a fraction.

Irrational numbers are squares of a number or any number that does not include a comparison(e.g division, fraction, ratio, etcetera) of a value. For instance, the square root of 2 is an irrational number because it does not go on indefinitely.

Answer:

see explanation

Step-by-step explanation:

the centroid is where the medians intersect.

On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.

(3)

GF = [tex]\frac{1}{2}[/tex] CG = [tex]\frac{1}{2}[/tex] × 14 = 7

CF = CG + GF = 14 + 7 = 21

(4)

GD = [tex]\frac{1}{3}[/tex]  AD = [tex]\frac{1}{3}[/tex] × 45 = 15

AG = 2 × GD = 2 × 15 = 30

(5)

GE = 2 × BG , that is

9x = 2(3x + 6) = 6x + 12 ( subtract 6x from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

The amount of money that Suzie will make over the four weeks is; $1856

Suzie will make a profit of:

The first week =  $300

The second week =  (300 * 30%) + 300 = $390

The third week = 390 * (1430%) = $507

The fourth week: 507 × (1430%) = $659.1

Thus, Sum of profit = $300 + $390 + $507 + $659.1

Sum of Profit = $1856.1 ≈ $1856

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Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.

In this situation we have a composite figure formed by two concentric circles, whose area ratio is presented below, in which the area is directly proportional to the square of radius:

[tex]\frac{A'}{A} = \frac{(R-r)^{2}}{r^{2}}[/tex]

2 · r² = (9-r)²

2 · r² = 81 - 18 · r + r²

r² + 18 · r - 81 = 0

The roots of the second order polynomial are r₁ = -9 + 9√2 and r₂ = -9 - 9√2. As radius is a non-negative number, the only root that is reasonable is r₁ = -9 + 9√2 (r₁ ≈ 3.728).

Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.

The image is missing and is thus included in the figure attached below.

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The proportion of sophomores that do not own a car is equal to 0.93.

Ratio is a mathematical expression that is used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

The proportion of sophomores that do not own a car is given by:

Therefore, proportion = 398/427 = 0.93.

The proportion of all students who are seniors who own cars is given by:

Therefore, proportion = 123/1192 = 0.10.

The proportion of non-car owners who are juniors is given by:

Therefore, proportion = 339/976 = 0.35.

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Complete Question:

At Central High School, there are 398 sophomores who do not own a car and 29 who do. There are 64 juniors who own a car and 339 who do not. There are 123 seniors who own a car, compared to 239 who do not. The above is a two-way table depicting this situation. Complete the following statements below by finding the ratio, then converting to a decimal. Round to the nearest hundredth.

The proportion of sophomores that do not own a car is?

The proportion of all students who are seniors who own cars is?

The proportion of non-car owners who are juniors is?

The number of eggs sold on Tuesday is 2 complete circles, while the number of eggs sold on Wednesday is 2 complete circles and 1 quarter of the circle.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

Given on Monday the shop sold 18 eggs. Therefore, each quarter of the circle represents 3 eggs.

Hence, the number of eggs sold on Tuesday is 2 complete circles, while the number of eggs sold on Wednesday is 2 complete circles and 1 quarter of the circle.

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[tex]\text{Given that,}~\\\\f(x) =a^x\\\\\text{L.H.S}\\\\=f(m+n+p)\\\\=a^{m+n+p}\\\\\text{R.H.S}\\\\=f(m) \cdot f(n) \cdot f(p)\\\\=a^m \cdot a^n \cdot a^p\\\\=a^{m+n+p}\\\\ \text{L.H.S} = \text{R.H.S}\\\\\text{Proved.}[/tex]