A textbook store sold a combined total of 426 math and sociology textbooks in a week. The number of math textbooks sold was 46 more than the number of sociology textbooks sold. How many textbooks of each type were sold?

Answer:

Step-by-step explanation:

5=cx-ax=x(c-a)

x(c-a)/5=1

(c-a)/5=1/x

x=5/(c-a)

Answer:

14 and 19

Step-by-step explanation:

14+5=19

14+19=33

Let's consider what the question asks for:

   --> the length of 'y'

To solve:

 --> we need to use trigonometry

     --> let's determine which function to use based on the image given

           below

         --> (look at image attached)

Let's use angle with measure of 53:

 --> the side with length of 'y' is adjacent to it

       [tex]cos(53)=\dfrac{y}{10} \\\\y=10*cos(53)=6.02[/tex]

Thus the length of that particular side is about:

 --> 6.0

Answer: 6.0

a. The number of pizzas the pizzeria must sell today for employees to receive the bonus will be 78 pizza.

b. The percent decrease in the number of pizzas sold today compared to yesterday is 7.69%.

a) To determine the number of pizzas the pizzeria must sell today for employees to receive the bonus, we need to calculate 20% of the 65 pizzas sold yesterday. 20% of 65 pizzas is 0.20 * 65 = 13. So, the pizzeria must sell 65 + 13 = 78 pizzas today for employees to receive the bonus.

b) To calculate the percent increase or decrease in the number of pizzas sold today compared to yesterday, we need to divide the difference between the two days' sales by the number of pizzas sold yesterday and multiply by 100.

((60 - 65) / 65) * 100

= (-5 / 65) * 100

= -7.69%

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The cost of one pound of potato is 0.73 pounds.

The mathematical field of algebra assists in the depiction of problems or conditions as mathematical statements. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

Now in the given question , we have to find the cost of one pound of potato.

here we have to find the cost of one pound of potato mia bought.

she total spent $3.65 for them and bought five pounds of potatoes.

cost of one pound of potato

= [tex]\frac{total spent}{total bought} = \frac{3.65}{5} =0.73 pounds[/tex]

 hence, cost of one pound of potato is 0.73 pounds.

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The approximate arc length is 56.52mm.

What is an arc length?

The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc section by simulating it with connected line segments. There are a finite number of segments in the rectification of a rectifiable curve.

Here, we have

Given: A bicycle wheel has a radius of 225 mm and has 25 equally spaced spokes.

To solve this question, we have to use the formula of the length of an arc which is given as

L = θ/360 * 2πr

To find the angle between each spoke, let's divide 360 by 25

θ = 360/25

θ = 14.4

Now that we have the value of the angle, let's substitute it and solve for the length of the arc.

L = 14.4/360 * 2(22/7)(225)

L = 56.52mm

Hence, the approximate arc length is 56.52mm.

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The area of the given parallelogram is 12 cm².

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

The formula to calculate the area of a parallelogram can thus be given as,

Area of parallelogram = b × h square units

where b is the length of the base and h is the height

According to the given parallelogram ABCD, we have

Length of the base b = 5 + 9 = 14 cm

The height h = 8 cm

Area of parallelogram = b × h

Area of parallelogram = 14 × 8

Area of parallelogram = 112 cm²

Thus, the area of the given parallelogram is 12 cm².

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The question seems incomplete, the missing figure has been attached below.

Answer:

Step-by-step explanation:

We can use the formula for the future value of an annuity to find the amount you'll have in the account at the end of Year 6. An annuity is a series of equal payments made at equal intervals of time, and the future value of an annuity is the amount you'll have in the future if you invest those payments and earn a given rate of interest.

The formula for the future value of an annuity is:

FV = PMT * (((1 + r)^n - 1) / r)

where:

FV = future value of the annuity

PMT = annual payment amount

r = annual interest rate as a decimal

n = number of payments

In this case:

PMT = $1,500

r = 0.05

n = 6

Plugging in the values:

FV = $1,500 * (((1 + 0.05)^6 - 1) / 0.05)

FV = $1,500 * (1.328867 - 1) / 0.05

FV = $1,500 * 0.328867 / 0.05

FV = $1,500 * 6.577340

FV = $9,865.61

So, the amount in the account at the end of Year 6 will be $9,865.61. To find the last payment, we subtract this amount from the desired future value of $10,000:

$10,000 - $9,865.61 = $134.39

Therefore, your last payment will be $134.39.

The equation and solution that represents the number of bags of cans of aluminum cans for recycling that Sara collects, given that Miri collects 3x cans as Sara, is x = 123/3, which is 41.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

Mathematical expressions contain variables, constants, numbers, and values using mathematical operands.

Equations differ from mathematical expressions based on the use of the equation symbol (=).

The number of bags of aluminum cans collected by Sara = x

The number of bags of aluminum cans collected by Miri = 3x

3x = 123 bags

The equation representing the number of bags of cans Sara collects x = 123/3

x = 41 (123/3)

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The expression for its distance d (measured in feet) from the intersection t seconds later is d = x + 79200 t (feet)

Since the balloon is moving due east, we only need to consider its horizontal motion, ignoring its vertical motion at a constant altitude of 95 feet.

Let's call the initial distance of the balloon from the intersection x. The distance of the balloon from the intersection t seconds later can be found using the formula for distance traveled at a constant speed:

d = x + vt

where v is the speed of the balloon (15 miles per hour) and t is the time elapsed (in hours). To convert the speed from miles per hour to feet per second, we can multiply by the conversion factor of 5280 feet per mile:

d = x + (15 miles/hour) * (5280 feet/mile) * (t hours)

d = x + (15 * 5280) t feet

d = x + 79200 t feet

So the expression for the distance of the balloon from the intersection t seconds later is:

d = x + 79200 t (feet)

Note: In this expression, x represents the initial distance of the balloon from the intersection, which is unknown.

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The numeric value of the exponential function at x = 19.5 is given as follows:

f(19.5) = 178.41.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which:

Considering that f(4.5) = 25 and f(14) = 85, the two equations are given as follows:

Hence:

a = 25b^(-4.5).

Then the value of b is obtained as follows:

25b^(-4.5)b^(14) = 85.

b^(9.5) = 85/25

b = (85/25)^(1/9.5)

b = 1.14.

Then the value of a is obtained as follows:

a = 25 x (1.14)^(-4.5)

a = 13.86.

Then the function is defined as follows:

y = 13.86(1.14)^x.

At x = 19.5, the numeric value is given as follows:

y = 13.86(1.14)^19.5

y = 178.41.

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Gaining instructional control is an important aspect of teaching and behavior management.

Instructional control is a term used in behavior analysis to describe a situation in which a teacher or other instructional agent has established the conditions necessary for effective teaching to occur.

Here are some strategies that can help you gain instructional control:

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Answer:

To find the time it takes a car traveling at 40 mph to stop after covering a distance of 30 feet, we need to use the formula for distance, speed, and time, which is:

distance = speed * time

Rearranging the formula, we get:

time = distance / speed

Since the speed is in miles per hour (mph), we need to convert it to feet per second (fps). One mph is equivalent to 1.47 fps, so 40 mph is equivalent to 40 * 1.47 = 58.8 fps.

Now we can plug in the values for distance and speed into the formula:

time = 30 feet / 58.8 fps

time = 0.5104 seconds

Rounding to the nearest second, we get:

time = 0.51 seconds

So, it would take the car approximately 0.51 seconds to stop after traveling 40 mph.

Step-by-step explanation:

Answer:  do you need me to answer all or anthor example.

Step-by-step explanation:

I will answer

The mean number of domestic applicants that Jenny selects is exactly 9.5, and the standard deviation is approximately 1.932

Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.

This is a problem involving a hypergeometric distribution since we have a fixed population (all applicants), two groups within the population (domestic and international students), and a fixed number of samples (20 students to be admitted).

Let X be the number of domestic applicants that Jenny selects this year. Then X follows a hypergeometric distribution with parameters N = 80 (total number of applicants), K = 38 (number of domestic applicants), and n = 20 (number of students to be admitted).

The mean of X is given by μ = nK/N, and the standard deviation of X is given by,

σ = √(nK(N-K)/(N²(N-1))).

Substituting the given values, we get:

μ = (20 x 38)/80 = 9.5

σ = √(203842/(80² x 79)) ≈ 1.932

Therefore, the mean number of domestic applicants that Jenny selects is exactly 9.5, and the standard deviation is approximately 1.932.

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Answer:

The greatest integer solution to the inequality 1 < (c - 1)^2 ≤ 36 is c = 6.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A = l x w

A = 105.1m x 67.1m

A = 7052.21m

Convert to yds.

7052.21 / 0.9144  =  7712.4

To the nearest whole, the area is 7712 yds2.

351 and 1053 are the next terms of geometric sequence  13, -39, 117...

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The given series is 13, -39, 117..

We need to find the fourth and fifth terms of the sequence.

The given sequence is geometric sequence.

Geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The general term of sequence [tex]a_{n} =ar^{n-1}[/tex]

r is the common ratio

r=-39/13

=-3

a=13 first term

a₄=13(-3)³

a₄=13(-27)

Fourth term is 351.

Now plug in n as 5 to find 5th term.

a₅=13(-3)⁴

a₅=1053

Hence, the next two terms of geometric sequence are 351 and 1053.

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The ratio 10:35 can be simplified to 2:7.

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

The ratio 10:35 can be simplified to 2:7.

To simplify a ratio, you can divide both values by the greatest common factor. In this case, the greatest common factor of 10 and 35 is 5, so 10 divided by 5 is 2, and 35 divided by 5 is 7.

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Simply the following ratio 10:35

Answer:

1. The monthly premium for workers' compensation insurance for the Winston Tree Farm and Nursery can be calculated as follows:

Monthly payroll: $3,560 Base rate: $5.93 per $100 Rate per $1,000: $5.93 * 10 = $59.30 Premium: $3,560 / 1,000 * $59.30 = $209.51

So, the monthly premium for workers' compensation insurance is $209.51.

2. The amount that Takis Machine Shop will pay each year for workers' compensation insurance can be calculated as follows:

Old base rate: $9.40 per $100 New base rate: $10.40 per $100 Monthly payroll: $53,896.84 Old rate per $1,000: $9.40 * 10 = $94.00 New rate per $1,000: $10.40 * 10 = $104.00 Old premium: $53,896.84 / 1,000 * $94.00 = $5,045.65 New premium: $53,896.84 / 1,000 * $104.00 = $5,610.71 Increase in premium: $5,610.71 - $5,045.65 = $565.06

So, Takis Machine Shop will pay an additional $565.06 each year for workers' compensation insurance.

3.The real estate tax for the home in Madison County can be calculated as follows:

Market value: $590,000 Rate of assessment: 40% of market value = $590,000 * 0.4 = $236,000 Tax rate: 42.73 mills = 0.04273 Tax: $236,000 * 0.04273 = $10,130.68

So, the real estate tax for the home in Madison County is $10,130.68.

4. The fair market value of Vanesa Vasquez's Roth IRA at age 65 can be calculated as follows:

Contribution: $2,500 Years of contribution: 65 - 35 = 30 Annual interest rate: 7.4% Future value: $2,500 * (1 + 0.074)^30 = $29,706.74

So, the fair market value of her Roth IRA at age 65 is $29,706.74.

The amount of interest earned can be calculated as follows:

Future value: $29,706.74 Present value: $2,500 Interest earned: $29,706.74 - $2,500 = $27,206.74

So, Vanesa Vasquez will have earned $27,206.74 in interest.

5. The interest rate as a percent for the GNMA Mortgage issue bond can be calculated as follows:

Face value: $10,000 Selling price: $10,000 * 103.7% = $10,370.00 Yield: 8.75% Price: $10,370.00 Interest: $10,370.00 - $10,000 = $370.00 Interest rate: ($370 / $10,000) * (12 / 1) = 0.09375 = 9.375%

So, the interest rate for the GNMA Mortgage issue bond is 9.375%, rounded to the nearest hundredth of a percent.

6. Let's call the number of days that Ricardo has to pay back the loan "d".

The interest on the loan can be calculated using the formula:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed, $2,500), r is the annual interest rate as a decimal (7.8% as a decimal is 0.078), and t is the time in years (d divided by 365).

So we have:

I = $2,500 * 0.078 * (d / 365)

We also know that the maturity value of the loan is the sum of the principal and the interest:

$2,548.75 = $2,500 + I

So we can substitute for I:

$2,548.75 = $2,500 + $2,500 * 0.078 * (d / 365)

Expanding the right-hand side:

$2,548.75 = $2,500 + $194.00 * (d / 365)

And solving for d:

d = 365 * ($2,548.75 - $2,500) / $194.00

d = 365 * ($48.75) / $194.00

d = 365 * 0.25191780821917808

d = 91.37 days

So Ricardo would have to pay back the loan in 91.37 days.

Step-by-step explanation:

The graph of ordered pairs (0, -5), (1, -3), (2, -1), (3, 1) is given below.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=2x-5.

Substitute x=0, 1, 2, 3, 4, ..... in the equation y=2x-5, we get

When x=0,

y=-5

When x=1,

y=-3

When x=2,

y=-1

When x=3

y=1

So, the ordered pair is (0, -5), (1, -3), (2, -1), (3, 1) and so on.

Therefore, the graph of ordered pairs (0, -5), (1, -3), (2, -1), (3, 1) is given below.

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Answer:

Option C. (x + 5)

Step-by-step explanation:

This quadratic equation can either be solved using the quadratic formula or be factorised using The Double Bubble Method.

Double Bubble Method:

After listing the different pairs of factors 10, the pair (that would add together to give 7) are 2 and 5. These two factors will be used to rewrite +7x:

[tex]x^{2} + 2x + 5x + 10[/tex]

Factorization by grouping (i.e factorising each separate group sharing a common factor) will then be applied:

[tex]= x(x + 2) + 5(x + 2)[/tex]

The common factor, which is the (x + 2) expression, will be extracted:
[tex]= (x + 2)(x + 5)[/tex]

∴ [tex]x^{2} + 7x + 10[/tex] can be factorised to [tex](x + 2)(x + 5)[/tex]

It is observed that a factor of the given quadratic equation is x + 5

∴Option C

Answer:

50

Step-by-step explanation:

4x10=40.

5x10=50

Answer:

Step-by-step explanation:

To increase a quantity in a given ratio, we can follow these steps:

Step 1: Find the total increase in the quantity.

Suppose the original number of books is "b". The total increase in the number of books is 40, so:

b + 40 = b

Step 2: Divide the total increase into two parts in the given ratio.

In this case, the ratio is 5:4, so we can divide the increase of 40 into two parts in the ratio 5:4. Let's call the first part "x". Then, the second part is 40 - x.

The first part (5x) is 5 times the second part (4x), so:

5x = 4(40 - x)

Step 3: Solve for x.

Expanding the right side:

5x = 160 - 4x

Adding 4x to both sides:

9x = 160

Dividing both sides by 9:

x = 40/9

Step 4: Find the new number of books.

The first part of the increase (x) is 40/9, and the second part (40 - x) is 40 - 40/9 = 40 * 9/9 - 40/9 = 40 * 8/9. The new number of books is the original number plus the two parts of the increase:

b + 40/9 + 40 * 8/9 = b + 40

So, the new number of books is b + 40.

Answer:

2

Step-by-step explanation:

Line MN ≅ Line LK

Since Line MN ≅ Line LK, that means the diagonals must be congruent ∴ MK ≅ NL.

Now that we know MK ≅ NL, we can set them equal to each other.

MK = [tex]16[/tex]

NL = [tex]7x + 2[/tex]

[tex]16=7x+2\\14=7x\\2=x[/tex]

Therefore, 2 is your final answer.

Answer:

[tex]\sf \dfrac{p}{q}=\dfrac{\pm1}{\pm1},\dfrac{\pm1}{\pm3},\dfrac{\pm7}{\pm1},\dfrac{\pm7}{\pm3}=\pm 1, \dfrac{\pm1}{\pm3},\pm 7, \dfrac{\pm7}{\pm3}[/tex]

Step-by-step explanation:

Given polynomial:

[tex]f(x)=-3x^3-5x^2+x-7[/tex]

If P(x) is a polynomial with integer coefficients and if p/q is a root of P(x), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).

Possible p-values

Factors of the constant term:  ±1, ±7

Possible q-values

Factors of the leading coefficient:  ±1, ±3

Therefore, all the possible values of p/q:

[tex]\sf \dfrac{p}{q}=\dfrac{\pm1}{\pm1},\dfrac{\pm1}{\pm3},\dfrac{\pm7}{\pm1},\dfrac{\pm7}{\pm3}=\pm 1, \dfrac{\pm1}{\pm3},\pm 7, \dfrac{\pm7}{\pm3}[/tex]

Substitute each possible rational root into the function:

[tex]x=-1 \implies f(-1)=-3(-1)^3-5(-1)^2+(-1)-7=-10[/tex]

[tex]x=1 \implies f(1)=-3(1)^3-5(1)^2+(1)-7=-14[/tex]

[tex]x=-7 \implies f(-7)=-3(-7)^3-5(-7)^2+(-7)-7=770[/tex]

[tex]x=7 \implies f(7)=-3(7)^3-5(7)^2+(7)-7=-1274[/tex]

[tex]x=-\dfrac{1}{3} \implies f\left(-\dfrac{1}{3}\right)=-3\left(-\dfrac{1}{3}\right)^3-5\left(-\dfrac{1}{3}\right)^2+\left(-\dfrac{1}{3}\right)-7=-\dfrac{70}{9}[/tex]

[tex]x=\dfrac{1}{3} \implies f\left(\dfrac{1}{3}\right)=-3\left(\dfrac{1}{3}\right)^3-5\left(\dfrac{1}{3}\right)^2+\left(\dfrac{1}{3}\right)-7=-\dfrac{22}{3}[/tex]

[tex]x=-\dfrac{7}{3} \implies f\left(-\dfrac{7}{3}\right)=-3\left(-\dfrac{7}{3}\right)^3-5\left(-\dfrac{7}{3}\right)^2+\left(-\dfrac{7}{3}\right)-7=\dfrac{14}{9}[/tex]

[tex]x=\dfrac{7}{3} \implies f\left(\dfrac{7}{3}\right)=-3\left(\dfrac{7}{3}\right)^3-5\left(\dfrac{7}{3}\right)^2+\left(\dfrac{7}{3}\right)-7=-70[/tex]

As f(p/q) ≠ 0, none of the possible rational roots are actual roots of the given polynomial.

The expression represents a degree five polynomial with four terms. The constant term is -6, the leading term is (1/2)x⁵, and the leading coefficient is 1/2.

A polynomial expression is an algebraic expression made up of variables and coefficients, combined using only the operations of addition, subtraction, and multiplication. The variables are raised to a power, which is a non-negative integer, and the coefficients are real numbers. A polynomial can have any number of terms, but it always has a degree, which is the highest power of the variables in the expression.

For the polynomial expression, (1/2)x⁵ - 6 - x⁴ - 5x⁴

There are 4 terms which are: (1/2)x⁵, - 6, - x⁴, and - 5x⁴.

The constant term is -6

The leading term is (1/2)x⁵

The coefficient of the leading term is 1/2.

In conclusion, the expression represents a degree five polynomial with four terms. The constant term is -6, the leading term is (1/2)x⁵, and the leading coefficient is 1/2.

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Answer:

quadrinomial, 4, -6, 1/2x^5, 1/2

Step-by-step explanation:

quadrinomials are polynomials with 4 terms

constant is the number with no variable

leading term is the term at the beginning

leading coefficient is the number at the beginning

Answer:258 containers

Step-by-step explanation:

Simply,

16770/65=258.

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The expression that represents the cost to the border will be 16L - 8.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides.

Perimeter of the rectangle = 2(L + W) units

A rectangular fountain has a length of L meters and a width of 3 meters less than its length. Then the equations are given as,

W = L - 3

The perimeter of the rectangle is given as,

P = 2(L + L - 3)

P = 2(2L - 3)

P = 4L - 6

The amount of money that is required for bordering the fountain is given as,

⇒ 4 × [4L - 6] + 4 × 4

⇒ 16L - 24 + 16

⇒ 16L - 8

The expression that represents the cost to the border will be 16L - 8.

And the diagram is given below.

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