Given: log a 2 = 4, log a 3 = 5, log a 5 = 8. Find log a 60.
A. 2.9
B. 1.46
C. .32
D. 2.1​

Step-by-step explanation:

The center of the circle is (-2,-3)

The radius is 2 since the distance from the center to the point on the circle is 2

Therefore the standard equation is

[tex](x + 2) {}^{2} + (y + 3) {}^{2} = 4[/tex]

Answer:

Set up the equation ... 60 + 40X = total charges... where X is the number of hours (6.5)

60 + 40(6.5) = ?

60 + 260 = ?

320 = total charges

Tom sold 27 raffle tickets and Steve sold 98 raffle tickets.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

Together, Steve and Tom sold 125 raffle tickets for their school.

Steve sold 17 more than three times as many raffle tickets as Tom.

Let s be the number of raffle tickets sold by Steve and t be the raffle tickets sold by Tom.

So,

3t + 17 + t = 125

4t = 108

t = 27

And s = 98

Therefore, Steve sold 98 and Tom sold 27 tickets.

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Probability of an event = (number of favorable event) / (total number of event).

P(B) = (Event B) / (total number of event).

Probability of getting 1 = 1/6.

Rolling dice is an independent event, it is not dependent on how many times it’s been rolled.

Probability of getting 1 three times in a row = probability of getting 1 first time × probability of getting 1 second time × probability of getting 1 third time.

Probability of getting 1 three times in a row = (1/6) × (1/6) × (1/6) = 1/216.

Hence, the probability of getting 1 three times in a row is 0.463%.

Answer:

10 miles

Step-by-step explanation:

Let's call the number of miles driven in a day "x". The total cost for Triangle Truck Rental can be expressed as:

Cost (Triangle) = $35 + 0.5x

The total cost for Circle Rent-A-Truck can be expressed as:

Cost (Circle) = $55 + 0.3x

We want to find the value of x such that Cost (Triangle) = Cost (Circle). So we can set the two expressions equal to each other and solve for x:

$35 + 0.5x = $55 + 0.3x

0.2x = $20

x = 100 miles

So the man would need to drive 100 miles in one day for both companies to have the same total cost.

The volume of the cylinder is  

Using the volume of cone given by the formula

= π r² h/3

In the problem the volume is given by  222 and volume of cylinder is equal to

= π r² h

comparing the two volumes and taking proportions

volume of cone / volume of cylinder

π r² h/3 / π r² h = 222 / volume of cylinder

π r² h / 3 π r² h = 222 / volume of cylinder

1 / 3  = 222 / volume of cylinder

volume of cylinder = 3 * 222

volume of cylinder =  666

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45 and 27.6 degrees are the two complementary angles.

When the right angle is split into two equal parts, each angle is 45°. A 45-degree angle is considered sharp. It is a right angle of half, or a 90-degree angle.

Angles that are complementary are those whose sum is 90 degrees. If the smaller angle has a measure of x, then the complementary angle's measure is 90 - x.

The issue shows that the greater angle (x + 17.4) is 17.4 degrees larger than the corresponding angle's measurement (90 - x). To find x, we can construct the following equation:

x + 17.4 = 90 - x + 17.4

When we simplify and find x, we obtain:

2x = 55.2

x = 27.6

The greater angle's measure is x + 17.4 = 45 degrees, while the smaller angle's measure is x = 27.6 degrees.

The two complementary angles are 27.6 and 45 degrees as a result.

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1,755 cm² icings are needed for one cake.

The correct option is (C).

What is the area of the circle?

The area of a circle is the amount of space enclosed within the circle. It is a measure of the size of the circle, and it is determined by the distance from the center of the circle to its edge (which is the radius). The formula for the area of a circle is:

A = πr²

The surface area of the circular top of the cake can be found using the formula for the area of a circle:

A = πr^2

where A is the area of the circle, and r is the radius. For the red velvet cake, the radius is 13 cm, so the area of the circular top of the cake is:

A = 3.14 x 13^2 = 530.66 cm^2 (rounded to two decimal places)

To find the surface area of the curved side of the cake, we need to find the circumference of the circular base and multiply it by the height of the cake. The circumference can be found using the formula:

C = 2πr

where C is the circumference and r is the radius. For the red velvet cake, the circumference of the circular base is:

C = 2 x 3.14 x 13 = 81.64 cm (rounded to two decimal places)

So, the surface area of the curved side of the cake is:

A = C x h = 81.64 x 15 = 1224.60 cm^2 (rounded to two decimal places)

Therefore, the total surface area of the cake that needs to be iced (excluding the circular bottom) is:

530.66 + 1224.60 = 1755.26 cm^2 (rounded to two decimal places)

Rounding to the nearest square centimeter, we get that approximately 1755 cm^2 of icing is needed for one red velvet cake at the Bisecting Bakery.

Therefore, 1,755 cm² icings are needed for one cake.

The correct option is (C).

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The height of the tulip sculpture is 66 inches, which is twice the height of the sunflower sculpture.

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

Sunflower = 33 inches

Tulip = Twice of sunflower

Using the above as a guide, we have the following:

Tulip = 2 * Sunflower

substitute the known values in the above equation, so, we have the following representation

Tulip = 2 * 33

Evaluate

Tulip = 66

Therefore, the height of the tulip sculpture is 66 inches.

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The closest answer choice is 0.76, which corresponds to 0.1934. So the answer is 0.1934.

We can calculate the variance of the hotel's star rating by using the formula:

variance = sum[(xi - mean)^2 * pi]

where xi is the rating (1, 2, 3, or 4), mean is the expected value of the rating, and pi is the proportion of the population that left that rating. Since we know the proportions of the population that left each rating, we can calculate the expected value of the rating as:

mean = 1(0.3) + 2(0.2) + 3(0.2) + 4(0.3) = 2.9

Then, we can calculate the variance as:

variance = (1 - 2.9)^2 * 0.3 + (2 - 2.9)^2 * 0.2 + (3 - 2.9)^2 * 0.2 + (4 - 2.9)^2 * 0.3

variance ≈ 0.57

Finally, the standard deviation is the square root of the variance:

standard deviation = sqrt(0.57) ≈ 0.756

Therefore, the closest answer choice is 0.76, which corresponds to 0.1934.

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P1(\stackrel{x_1}{6}~,~\stackrel{y_1}{3})\qquad P2(\stackrel{x_2}{-3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ P1P2=\sqrt{(~~-3 - 6~~)^2 + (~~5 - 3~~)^2} \implies P1P2=\sqrt{( -9 )^2 + ( 2 )^2} \\\\\\ P1P2=\sqrt{ 81 + 4 } \implies P1P2=\sqrt{ 85 }[/tex]

Answer:

x=5

Step-by-step explanation

4x=x+15

x=5

Answer:

Since ABCD is a kite, AB=AD and BC=CD

Given:

AB = 4x

AD = x + 15

equating both sides;

4x = x + 15

4x - x = 15

3x = 15

x = 15/3

x = 5

Answer:

4 I think

Step-by-step explanation:

4+36=40, 10x4=40

Answer: 12

Step-by-step explanation:

1) Create an equation. Lets call the missing number x. 36 is added to x or 36+x and when 36 is added to x it is 4 times of x or 4x, so our equation is 36+x=4x.

2) Bring the variable to one side by subtracting x on both sides. Our new equation is 36=3x.

36) Get rid off the coefficient 3 by dividing 3 on both sides to get x=12

On solving the provided question, we can say that The percentage (P) = 34%

A percentage in mathematics is a figure or ratiο that is stated as a fractiοn of 100. The abbreviations "pct.," "pct," and "pc" are alsο οccasionally used. It is frequently denoted using the percent symbοl "%," though. The amount of percentages has nο dimensions. With a denominatοr of 100, percentages are basically fractiοns.

To shοw that a number is a percentage, place a percent symbοl (%) next to it. Fοr instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To cοmpute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.

the total frequency:

Total = 29+53+50+22+1

Total = 155

The proportion (p)

p = f/total

The percentage (P)

P = p × 100

P =0.34 × 100 = 34%

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A rectangle's length is 4 inches greater than its breadth.. If the perimeter of the rectangle is 36. Area will be 77[tex]cm^{2}[/tex].

A quadrilateral with in all four of its angles being right angles is a rectangle. A quadrilateral with four right angles and four equal-length sides is called a square. As a result, a square is indeed a particular form of rectangle since it has rectangles with equal-length sides.As a result, a square is indeed a particular form of rectangle since it has rectangles with equal-length sides. Because a square is indeed a quadrilateral with in all four angles at right angles, every square is also a rectangle. To be a square, a rectangle's sides must all be the same length, hence not all rectangles are squares.

Finding the Area , we obtain:

Let the rectangle's breadth be x cm.

Its length is then x+4 cm.

According to the problem,

2{x+x+4}=36

or, 2x+4=18

or, x=7.

So, breadth  is 7 cm and length is 11 cm.

So, the area  is 7×11=77 [tex]cm^{2}[/tex].

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The required volume of the given rectangular prism is given as 240 in ³.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
From the data we have,
Length of the rectangle prism = 12 in
Width of the rectangle prism = 2 in
Height of the rectangle prism = 10 in

The volume of the rectangular prism = length × width × height
                                                 = 12 × 2 × 10
                                                 = 240 in ³

Thus, the required volume of the given rectangular prism is given as 240 in ³.

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The question is incomplete.
Complete question is," Calculate the volume of the prism of dimensions length, width and height are 12, 2, and 10 respectively. "

Hannah’s brother counted correctly it Hannah gave him & 8 pennies and 12 nickels.

The concept of an equation in algebra is a mathematical declaration that demonstrates the equality of two mathematical expressions. Declaration of equivalence between two expressions made up of numbers or variables

Finding the counted the money correctly , we obtain:

x= number of pennies

y = number of nickels.

x + y =20

so , x = 20-y

x+5y = 68

20-y +5y = 68

4y= 48 so y = 12 and x = 8.

8 pennies and 12 nickels

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a. The vertex form of its equation is,  y = a(x-1)² + 16

b. The value of x is, 7

c. The equation of the axis of symmetry is,  x = 1

d. The domain and range are respectively, all real values of x and y ≤ 16

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

a. The vertex form of a quadratic equation is given by y = a(x-h)²+ k, where (h, k) is the vertex of the parabola.

From the given information, we know that the vertex is at (1, 16), so the equation in vertex form is y = a(x-1)² + 16.

b. We are given that the parabola has one root at (-5, 0) and another root at (x, 0). Since the parabola is symmetric about the axis of symmetry, the x-coordinate of the vertex must be the midpoint of -5 and x. Using the midpoint formula, we get:

(-5 + x)/2 = 1

Solving for x, we get x = 7.

c. The axis of symmetry of a parabola is the vertical line that passes through the vertex. In this case, the vertex is at (1, 16), so the equation of the axis of symmetry is x = 1.

d. The domain of a quadratic function is all real numbers, since the function is defined for all values of x. The range of this function is y ≤ 16, since the vertex is at (1, 16) and the parabola opens downward.

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The value of AD is 26.

There are two circles with centers A and D.

The tangent line touches both points B and C.

The given measurements are enough to solve for the missing value and the solution is shown below:

Solve for the measurement of AC which the hypotenuse of legs AB and BC by Pythagorean theorem:

Solve for angle of A

sin A=26/27.51

A=70.93°

Finally, we solve for the length of AD using SOH

sin 70.93°=AD/27.51

AD=26

The answer is 26.

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The total interest charges after 30 years with an APR of 3.4 % is given by the equation A = $ 77,550.80

The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. An APR is a number that represents the total yearly cost of borrowing money, expressed as a percentage of the principal loan amount.

Given data ,

Let the total interest charges after 30 years be represented as A

Now , the equation will be

The APR percentage = 3.4 %

The amount taken as loan = $ 130,000

The number of years = 30 years

The monthly payment = $ 576.53

The number of payments n = 30 x 12 = 360 payments

So , the total amount paid in 30 years = monthly payment x number of payments

Substituting the values in the equation , we get

The total amount paid in 30 years = 360 x 576.53

The total amount paid in 30 years = $ 207,550.80

Now , the total interest charges after 30 years A = total amount paid in 30 years - amount taken as loan

Substituting the values in the equation , we get

The total interest charges after 30 years A = $ 207,550.80 - $ 130,000

On simplifying the equation , we get

The total interest charges after 30 years A = $ 77,550.80

Hence , the interest charges after 30 years is $ 77,550.80

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Lets solve ~

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} = 10[/tex]

[ taking square root on both sides ]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} } = \sqrt{10} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \pm \sqrt{10} [/tex]

Both the values are appropriate here, as the square of both negative or positive value is same [positive value]

[tex] \huge\bold \large \bf{Solution }[/tex]

[tex] \rightarrow \large \displaystyle \sf \: {x}^{2} = 10 \: [/tex]

Transposing square on RHS , We get

[tex]\rightarrow \large \displaystyle \sf \: x \: = \sqrt{10} [/tex]

We know that,

10 does not even have a square root , so,

[tex]\rightarrow \large \displaystyle{\bf{ \pink{x \: = \pm \: \sqrt{10} }}}[/tex]

We know that the value of root is both negative and positive.

[tex] \purple {\rule{190pt}{4pt}}[/tex]

The volume of the rectangular prism is 42 cubic inches

The volume of a rectangular prism is calculated as the product of its length, width, and height.

The formula is:

V = l x w x h

Where,

V is the volume

l is the length

w is the width

h is the height.

The volume of this figure is calculated using the formula given above as;

V = l * w * h

We can divide the figure into two rectangular prism and calculate the volume.

v = (8 * 3 * 1) + (6 * 3 * 1)

v = 42 in³

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Using angle relationships, the missing measures are:

m<3 = 138 degrees.

m<5 = 42 degrees.

m<8 = 138 degrees.

Using angle relationships, each of the measure of the angles can be calculated as follows:

Given that, m<1 = 138 degrees.

m<3 = m<1 [vertical angles are congruent]

Substitute:

m<3 = 138 degrees.

m<5 + m<3 = 180

Substitute:

m<5 + 138 = 180

m<5 = 180 - 138

m<5 = 42 degrees.

m<8 = m<3 [alternate interior angles are congruent]

m<8 = 138 degrees.

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The order of the rectangular area from greatest to least is green sticker > yellow sticker > red sticker

The area of a rectangle is calculated by multiplying its length by its width. So if the length of a rectangle is l and the width is w, then its area A is given by the formula A = l x w.

To solve this problem, we can find the area of each sticker one after the other.

Area = length * width

1. red sticker = 2 * 1.5 = 3cm²

2. green sticker = 12 * 0.5 = 6cm²

3. yellow sticker = 3 * 1.25 = 3.75cm²

The order is green sticker > yellow sticker > red sticker

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Answer:

40 hours

26.09 hours

Step-by-step explanation:

What is the driving time for a ​1800-mile trip if you drive at an average speed of 45 miles per​ hour?

1800 / 45 = 40 hours

What is the driving time at 69 miles per​ hour?

1800 / 69 = 26.09 hours

Step-by-step explanation:

The driving time for a 1800-mile trip at an average speed of 45 miles per hour can be calculated as

Driving time = Total distance / Average speed

Driving time = 1800 miles / 45 miles per hour = 40 hours

Similarly, the driving time at an average speed of 69 miles per hour can be calculated as:

Driving time = 1800 miles / 69 miles per hour = 26 hours

So if you drive at an average speed of 45 miles per hour, the driving time for a 1800-mile trip would be 40 hours, and if you drive at an average speed of 69 miles per hour, the driving time would be 26 hours.

The measure of angle ∠T found using the law of sines is about 72°

The law of sines states that the ratio of the of the sine of an angle in a triangle to the length of the opposite side, is the same for the three angles in a triangle.

Mathematically, where the side lengths of the triangle are; a, b, c, and the corresponding opposite angles are ∠A, ∠B, and ∠C, we get;

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

The parameters in the question are;

AT = 28

AD = 37

m∠D = 46°

DT = a

Therefore, according to the law of sines, we get;

37/(sin∠T) = 28/(sin(46°))

Inverting both sides, we get;

(sin∠T)/37 = (sin(46°))/28

(sin∠T) = 37 × (sin(46°))/28

∠T = arcsine(37 × (sin(46°))/28) ≈ 72°

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The expression which is equivalent to the expression 14x+3−13x+(−2) is:

x +1

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

14x+3−13x+(−2)

Now it can be simplify in the following way:

⇒ 14x - 13x + 3 - 2

the variable and constant terms can be clubbed together,

⇒ x + 1

Hence, the equivalent expression is x + 1

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1) Based on the percentage of the downpayment, the total payment made for the store item is $1,100, which includes a finance charge or interest of $100.

2) The monthly payment for 12 installments is $87.50.

The total cost of the item is based on the downpayment's equivalent percentage (proportion).

A proportion is the equation of two or more ratios.

Finance Charge (Interest) = $100

Downpayment = $50 or 5%

Installment period = 12 months

Cost of item = $1,000 ($50/5%)

Total payment = $1,100 ($1,000 + $100)

Monthly payment = $87.50 ($1,100 - $50)/12

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The downpayment is 5% of the total cost of the item.

Answers

9x+6x=2600

15x=2600

x=520/3

9x=9×520/3=1560

6x=6×520/3=1040