Letter B is plotted at (3,-2). True Or False

9514 1404 393

Answer:

  0.984

Step-by-step explanation:

Nine hundred eighty-four thousandths is 0.984.

__

The least-significant digit of the numerator goes in the number place with the place value 1/1000. The more significant digits are then placed to the left of that in the usual way.

The probability that a point chosen at random lies on the shaded region is given as follows:

4/7.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The area of the shaded region in this problem is given as follows:

4² = 16.

The total area of the figure is given as follows:

16 + 2 x 1/2 x 3 x 4 = 28.

Hence the probability is given as follows:

16/28 = 4/7.

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Answer:

  Miriam

Step-by-step explanation:

Miriam, with her lower FICO score, is more likely to have been offered the loan with the higher interest rate.

Answer:

2

Step-by-step explanation:

Answer:

correct

Step-by-step explanation:

Hope this help!!!

Have a nice day!!!

The recursive formula for this problem is given as follows:

\(P_n = 1.05 \times P_{n - 1}\)

The explicit formula for this problem is given as follows:

\(P_n = 150(1.05)^n\)

The number of tickets in 2026 is given as follows:

297 tickets.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number which is defined as the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n}\)

In which \(a_1\) is the first term.

The parameter values for this problem are given as follows:

\(a_1 = 150, q = 1.05\)

Hence the function is given as follows:

\(P_n = 150(1.05)^n\)

2026 is 14 years after 2012, hence the number of tickets is given as follows:

\(P_{14} = 150(1.05)^{14} = 297\)

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Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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The transformations which is NOT preserve the size and the shape of the figure is dilate by a scale factor of 4 (B) and dilate by a scale factor of 1 (C).

Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.

When a figure is dilated, the size of the original figure is changed.

A figure is graphed in the coordinate plane. Let's check all the option for the transformation of original figure.

Hence, the transformations which is NOT preserve the size and the shape of the figure is dilate by a scale factor of 4 (B) and dilate by a scale factor of 1 (C).

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Answer:

y=1/2x+11

Step-by-step explanation:

use the slope of one half and the point and put them into point slope form.

y-y1 = m(x-x1) or y-16 = 1/2(x-10), distribute 1/2

y-16=1/2x - 5, add 16 to both sides

y = 1/2x + 11

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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Answer:

17

Step-by-step explanation:

Properties used:-

All sides of rhombus are equal therefore in the triangles

EQUAL SIDE OPPOSITE TO ANGLES, ANGLES BECOME EQUAL

then we use alternate interior angles

Then we get,

3x-11=x+23

2x=34

x=17

We have to Find:

\( \sf \longmapsto5^{ - x }= 6\)

Let's start.

\( \sf \longmapsto log(5^{-x}) = log(6) \)

\( \sf \longmapsto - x \: log(5) = log(6)\)

\( \sf \longmapsto - x = \dfrac{ log(6) }{ log(5) } \)

\( \sf \longmapsto \: x = \dfrac{ -log(6) }{ + log(5)} \)

Done

Answer:

Step-by-step explanation:

Given point (2, -7)

Translation rule T₍₋₃,₁₎

Translated point is:

Point (-1, -6) is located in the quadrant III as both coordinates are negative

Correct option is C

Answer:

\(BC=5.1\)

\(B=23^{\circ}\)

\(C=116^{\circ}\)

Step-by-step explanation:

The diagram shows triangle ABC, with two side measures and the included angle.

To find the measure of the third side, we can use the Law of Cosines.

\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)

In this case, A is the angle, and BC is the side opposite angle A, so:

\(BC^2=AB^2+AC^2-2(AB)(AC) \cos A\)

Substitute the given side lengths and angle in the formula, and solve for BC:

\(BC^2=7^2+3^2-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-42\cos 41^{\circ}\)

\(BC^2=58-42\cos 41^{\circ}\)

\(BC=\sqrt{58-42\cos 41^{\circ}}\)

\(BC=5.12856682...\)

\(BC=5.1\; \sf (nearest\;tenth)\)

Now we have the length of all three sides of the triangle and one of the interior angles, we can use the Law of Sines to find the measures of angles B and C.

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

In this case, side BC is opposite angle A, side AC is opposite angle B, and side AB is opposite angle C. Therefore:

\(\dfrac{\sin A}{BC}=\dfrac{\sin B}{AC}=\dfrac{\sin C}{AB}\)

Substitute the values of the sides and angle A into the formula and solve for the remaining angles.

\(\dfrac{\sin 41^{\circ}}{5.12856682...}=\dfrac{\sin B}{3}=\dfrac{\sin C}{7}\)

Therefore:

\(\dfrac{\sin B}{3}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin B=\dfrac{3\sin 41^{\circ}}{5.12856682...}\)

\(B=\sin^{-1}\left(\dfrac{3\sin 41^{\circ}}{5.12856682...}\right)\)

\(B=22.5672442...^{\circ}\)

\(B=23^{\circ}\)

From the diagram, we can see that angle C is obtuse (it measures more than 90° but less than 180°). Therefore, we need to use sin(180° - C):

\(\dfrac{\sin (180^{\circ}-C)}{7}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin (180^{\circ}-C)=\dfrac{7\sin 41^{\circ}}{5.12856682...}\)

\(180^{\circ}-C=\sin^{-1}\left(\dfrac{7\sin 41^{\circ}}{5.12856682...}\right)\)

\(180^{\circ}-C=63.5672442...^{\circ}\)

\(C=180^{\circ}-63.5672442...^{\circ}\)

\(C=116.432755...^{\circ}\)

\(C=116^{\circ}\)

\(\hrulefill\)

Additional notes:

I have used the exact measure of side BC in my calculations for angles B and C. However, the results will be the same (when rounded to the nearest degree), if you use the rounded measure of BC in your angle calculations.

Answer:

\(y = {x}^{2} - 2\)

Or if you want with the value of h too.

\(y = {(x - 0)}^{2} - 2\)

Step-by-step explanation:

\(y = a {(x - h)}^{2} + k\)

Find the value of h and k by using the formula.

\(h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a} \)

From y = x²-2

\(a = 1 \\ b = 0 \\ c = - 2\)

Substitute these values in the formula.

\(h = - \frac{0}{2(1)} \\ h = 0\)

Therefore, h = 0.

\(k = \frac{4(1)( - 2) - {0}^{2} }{4(1)} \\ k = \frac{ - 8}{4} \\ k = - 2\)

Therefore, k = - 2.

From the vertex form, the vertex is at (h, k) = (0,-2). Substitute h = 0, a = 1 and k = -2 in the equation.

\(y = a {(x - h)}^{2} + k \\ y = 1 {(x - 0)}^{2} - 2 \\ y = {(x)}^{2} - 2 \\ y = {x}^{2} - 2\)

These type of equation where b = 0 can also be both standard and vertex form.

Answer:

\((x^2-3^2)(x+3)\)

\((x-3)(x+3)(x+3)\)

\((x-3)(x+3)^2\)

Step-by-step explanation:

Given

\((x^2-9)(x+3)\)

Required

Select 3 equivalent expressions

\((x^2-9)(x+3)\)

Express 9 as 3^2

\((x^2-3^2)(x+3)\) --- This is one equivalent expression

Take \(x^2 - 3^2\) as difference of two squares

\((x-3)(x+3)(x+3)\) -- This is another equivalent expression:

Solving further:

\((x-3)(x+3)(x+3)\) becomes

\((x-3)(x+3)^2\)   -- This is another equivalent expression:

Hence, the equivalent expressions are:

\((x^2-3^2)(x+3)\)

\((x-3)(x+3)(x+3)\)

\((x-3)(x+3)^2\)

The first debt that Alice would have to pay based on the Stack method would be the third debt. Option C

From the stack method, the debt that Alice would have to pay off first would be the debt that has the highest interest rate.

The amount of 150 dollars would then be added to the debt that has the second highest rate.

Hence the amount of debt that would be paid off first would be the first debt based on the stack method.

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The value of x in the equation 4 x plus 8 y equals 40 is 8.4

The equation is given as:

4 x plus 8 y equals 40

Rewrite the equation as:

4x + 8y = 40

The value of y is 0.8.

So, we have:

4x + 8 * 0.8 = 40

Divide through by 4

x + 2 * 0.8 = 10

Evaluate the product

x + 1.6 = 10

Subtract 1.6 from both sides

x = 8.4

Hence, the value of x in the equation 4 x plus 8 y equals 40 is 8.4

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The unit rate is 4 passengers per car

We need to find the unit rate.

576 passengers in 144 cars

rate = 576/144

rate = 4 passengers per car

Therefore, the unit rate is 4 passengers per car

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The monthly payment by ignoring intrest and rouning down the amount owed is $104

Given that "you have a $3125 student loan. suppose you pay the loan off in two and a half years(30 months)" and asked to find out the monthly payment by ignoring the intrest and round off the amount to nearest integer.

Total loan=$3125 .

Total time given= two and a half years(30 months)

The monthly payment=\(\frac{3125 }{30}\)

The monthly payment=$104

To complete the student loan monthly payment of $104 is required.

Therefore,The monthly payment by ignoring intrest and rouning down the amount owed is $104

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Answer:

\(y +2 =-6(x - 1)\)

Step-by-step explanation:

Given

\((x_1,y_1) = (1,-2)\)

\(m=-6\)

Required

Determine the point slope equation

This can be determined using the following formula:

\(y - y_1 =m(x - x_1)\)

Where:

\((x_1,y_1) = (1,-2)\)

\(m=-6\)

So, we have:

\(y - (-2) =-6(x - 1)\)

This gives:

\(y +2 =-6(x - 1)\)

Hence, the point slope form is \(y +2 =-6(x - 1)\)

The leading coefficient of the expression is 1

From the question, we have the following parameters that can be used in our computation:

4x² + x4 -8 -5

When written in standard form, we have

x^4 + 4x^2 - 8 - 5

Evaluate the like terms

x^4 + 4x^2 - 13

The leading coeffiicient is the coefficient of the term with highest power

In this case, it is

Coefficient = 1

Hence, the value is 1

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Using the system of equations and use the elimination method the two numbers are 82 and 48.

What is the elimination method?

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are equal.

Here, we

let the first number = x

let the second number = y

according to the given conditions:

x + y = 130 ........(1)

x - y = 34 .........(2)

Using the elimination method we add both equations (1) and (2) and we get

2x = 164

x = 164/2 = 82

Now, we substitute the value of x in eq (1) and we get

82 + y = 130

y = 130-82

y = 48

Hence, using the system of equations and use the elimination method the two numbers are 82 and 48.

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3²×3^-5

Multiply the terms with the same base by adding their exponents

3²-5

Calculate the differences

3^-³

Express with a positive exponent using  a ^-n =1/n

                                                                             a

1/3³

Write the exponentiation as a multiplication

3×3×3

Multiply the numbers

27

Answer is 1/27

The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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Answer: (x+6)(x-3)

Step-by-step explanation:

y=x^2+3x-18

(x+6)(x-3 )