Plot 7/10 and 1 1/5 on the number line below.

Answer: 21

Step-by-step explanation:

Answer: y = -3x + 5

Step-by-step explanation:

We are given that the line passes through the point (1,2) and has a slope of -3. To find the y-intercept, we can use the point-slope form of a line:

y - y1 = m(x - x1)

where (x1, y1) is the point the line passes through.

Substituting the values we have:

y - 2 = -3(x - 1)

Expanding the brackets and rearranging:

y - 2 = -3x + 3

y = -3x + 5

Therefore, the equation of the line is y = -3x + 5, in slope-intercept form.

The decimal time 0.8 seconds can be said as: A. Zero point eight seconds

In Algebra, decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point. For example, 34.5 is a decimal number.

A decimal number is normally read by saying the whole part of it as a whole number and by individually reading out every number after the decimal point. For example, 28.79 would be read as twenty-eight point seventy nine.

Thus, the decimal 0.8 seconds can be pronounced as:

Zero point eight seconds

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Answer:

1:2

2:1

3:3

Explanation:

1 on the left is with 2 on the right (1:2) because base and height are inversed, so the same explanation is for 2:1.

3:3 because the hypotenuse (the base) is calculated with the height of the right angles.

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The time it will take for the money in the account to reach $4,000 is about 15.407 years.

To solve for the number of years it takes for the amount in the account to reach $4,000, we need to solve the equation:

[tex]4000 = 2000e^{0.045t[/tex]

Dividing both sides by 2000, we get:

[tex]2 = e^{(0.045t)[/tex]

To solve for t, we can take the natural logarithm of both sides:

[tex]ln 2 = ln e^{(0.045t)[/tex]

Using the property that ln [tex]e^x = x[/tex], we can simplify this to:

[tex]ln 2 = 0.045t[/tex]

Dividing both sides by 0.045, we get:

t = (ln 2)/0.045

Using a calculator, we can evaluate this expression to get:

[tex]t = 15.407[/tex]

Therefore,  it will take about 15.407 years for the amount in the account to reach $4,000.

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Answer:

9 Prizes

Step-by-step explanation:

She begins with 420 tickets.

She goes on 2 rides for 75 tickets each so 420-75-75= 270

She then attends the concert for 180 tickets so 270-180= 90

Now she is left with 90 tickets. 10 tickets = 1 prize therefore you can do 90/10 = 9

9 PRIZES

Answer:

25%

Step-by-step explanation:

The class width is 0.3877.

In order to analyze data, it is often helpful to group it into categories, or intervals, and then determine how frequently each interval occurs. This process is known as frequency distribution.

To calculate the class width, you need to determine the range of each interval. The range is the difference between the upper and lower limits of the interval. For example, the first interval is 160-179, so the range is 179-160=19.

In mathematical terms, the formula for class width is:

Class Width = (Range of all intervals) / (Number of intervals)

In your case, the range of the intervals are:

19, 19, 19, 19, and 19

And the number of intervals is:

53 + 24 + 93 + 27 + 48 = 245

So, the class width can be calculated as follows:

Class Width = (19+19+19+19+19) / 245

Class Width = 95 / 245

Class Width = 0.3877

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Complete Question:

The data given below is for 245 randomly selected 10-minute intervals, where the number of people entering the atrium of a large mall were recorded. Calculate the class width.

Number of Guests         Frequency

160 - 179                                 53

180- 199                                 24

200 - 219                              93

220 - 239                              27

240 - 259                             48

The vector that satisfies the equation v = 2u - 3w, where u = (5, -4) and w = (4, -2), is v = (-2, -2).

A vector is a mathematical quantity that represents a magnitude (length) and direction in space, usually represented as an ordered set of numbers or coordinates, used to describe physical quantities and geometric objects.

An equation is a mathematical statement that indicates the equality of two expressions or quantities, often containing variables, used to describe relationships and solve problems in various fields of mathematics and science.

According to the given information:

To find the vector that satisfies the given equation:

v = 2u - 3w

we need to first calculate the vectors u and w using the given points:

u = (5 - 0, 1 - 5) = (5, -4)

w = (4 - 0, 3 - 5) = (4, -2)

Substituting these values into the equation:

v = 2u - 3w

v = 2(5, -4) - 3(4, -2)

v = (10, -8) - (12, -6)

v = (-2, -2)

Therefore, the vector that satisfies the given equation is (-2, -2).

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The solution to the system of equations shown above is: A. More than 1 solution.

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

3y - 3x = -9   ......equation 1.

4y - 4x=-12 ......equation 2.

Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which is given by multiple ordered pairs and as such, it has more than one solution or infinitely many solutions because the lines coincide.

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The correct option about the two data set's distribution is B) The distributions are somewhat similar.

Given that,

For data set 1,

Mean = 54 and MAD = 4

For data set 2,

Mean = 60 and MAD = 2

Means to MAD ratio = (60 - 54) / (2 - 4) = 6 / -2 = -3

So means to MAD ratio is -3, not 3.

Now, it is clear that the distributions are not fully similar.

But it appears to be somewhat similar since Mean absolute deviation is somewhat similar, which is close.

Hence the correct option is B.

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Answer:

Step-by-step explanation:

yees

a) There are 720 different ways to arrange all six tables in a row. b) There are also 15 other methods to select four of the six tables.

A combination is a technique for calculating the number of alternative arrangements in a set of objects where the order of the selection is irrelevant.

Given this,

Mrs. Smith wants to arrange six activity tables side by side in her classroom.

After aligning all six tables in a straight line, we can use the factorial function to compute the product of all positive integers up to a specified value. We could write:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

As a result, there are 720 different ways to arrange all six tables in a row.

And, to select four of the six tables, we can use the combination function, which computes the number of ways to select k things from n different items, regardless of their order. We could write:

⁶C₄ = 6! / (4! x 2!)

= (6 x 5 x 4 x 3 × 2 × 1) / [(4 x 3 x 2 x 1) × (2 × 1)]

= (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1)

= 15

As a result, there are 15 different methods to select four of the six tables.

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The probability that the randomly selected person attending the concert is an adult or has purchased the ticket in advance is 188/250.

We have,

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given a table which shows when the tickets for a concert are sold and the types of tickets that are sold.

The probability of A or B can be calculated as,

P(A or B) = P(A) + P(B) - P(A and B)

Let A denote the people is an adult.

Let B denote the people who has purchased the ticket in advance.

P(A) = 148/250

P(B) = 140/250

P(A and B) = 100/250

Probability that a randomly selected person attending the concert is an adult or has purchased the ticket in advance is,

P(A or B) = 148/250 + 140/250 - 100/250

              = 288/250 - 100/250

              = 188/250

Hence the required probability is 188/250.

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The expression   -2³a⁴b⁻⁵/ 24a⁷b³ × b¹⁰/a⁻²b⁻⁴ with no negative exponents is -a⁵b⁶/3

The given expression is -2³a⁴b⁻⁵/ 24a⁷b³ × b¹⁰/a⁻²b⁻⁴

a and b are the variable in the expression

We have to find the expression without negative exponents

[tex]\frac{a^m}{a^n}=a^m^-^n[/tex]

-8a⁴b⁻⁵/ 24a⁷b³ × b¹⁰/a⁻²b⁻⁴

-a³/3b⁸  × a²b¹⁴

-a⁵b⁶/3

Hence, the expression with no negative exponents is -a⁵b⁶/3

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The number of stamps that Jessica and Bonita have altogether if the percent increase in stamps with Bonita is 15% more is 2150.

Given that,

Bonita has 15 percent more stamps than Jessica.

Let x be the number of stamps that Jessica has.

Then,

Number of stamps that Bonita has = x + 150

x + 150 = x + 15% of x

x + 150 = x + (0.15)x

x + 150 = 1.15x

0.15x = 150

x = 1000

Hence the number of stamps that Jessica has = 1000

Number of stamps that Bonita has = 1150

Total number of stamps = 1000 + 1150 = 2150

Hence the total number of stamps is 2150.

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Answer:

take a photo of the question so I can answer it please

The degree solutions of the equation are 51.82 degrees and 128.17 degrees

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

cos² (x) + cos (x) − 1 = 0

Let y = cos(x)

So, we have

y² + y - 1 = 0

When solved graphically, we have

y = ±0.618

This means that

cos(x) = ±0.618

Take the arccos of both sides

x = cos-1(±0.618)

Evaluate

x = 51.82 degrees and 128.17 degrees

Hence, the angles are 51.82 degrees and 128.17 degrees

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-2 to -4 = multiply by 2

-4 to -12 = multiply by 3

-12 to -48 = multiply by 4

-48 to -240 = multiply by 5

Our next three terms will require us to multiply by 6, then 7, then 8.

-240 x 6 = -1440

-1440 x 7 = -10080

-10080 x 8 = -80640

Answer: C

Hope this helps!

Answer:

C

Step-by-step explanation:

multiply by 2     then by  3     then by  4   then by 5

   then by   6     then by  7   then by  8

Option 1, 3 and 6 are the proper subsets of the set U = {a, c, e, g, i, k}.

The subsets of U that do not include all of its components are the correct subsets of U. Given that it doesn't include any items of U, Option 1, A = empty set, is a valid subset of U. In the case of option 2, B = "a, c, e, g, i, k" is the set U itself and is not a legitimate subset of U because it contains all of U's components.

Now, option 4, D = {b, d, f, h}, is not a subset of U as it contains elements that are not in U. Option 5 is not correct as it includes both A and B, which is not a proper subset of U. In option 6, both 1 and 3 are given, hence, it is correct.

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Complete question - If U = {a, c, e, g, i, k} then which of the following are proper subsets of U?

Choose one  4 points

1. A = emptyset

2. B = {a, c, e, g, i, k}

3. C = {a, c, e, g}

4. D = {b, d, f, h}

5. Set A, set B and set C

6. Set A, and set C

paint 1 house in = 6 days

paint ? house in = 222 days

= 222 ÷ 6 = 37 houses

Answer: A painter can paint 37 houses in 222 days

Answer:

To determine the scale factor used to create the image, we need to compare the corresponding side lengths of the original triangle ABC and the dilated triangle A'B'C'.

Let's take the side AB of triangle ABC and its corresponding side A'B' of triangle A'B'C'. The length of AB is 18-9=9 units, while the length of A'B' is 6-3=3 units. Therefore, the scale factor for the dilation from triangle ABC to triangle A'B'C' is:

scale factor = length of A'B' / length of AB = 3/9 = 1/3

So the answer is: the scale factor used to create the image is one third.

Step-by-step explanation:

The scale factor used to create the image triangle A'B'C' is 1/4.

To determine the scale factor used to create the image, we can compare the corresponding side lengths of the original triangle ABC and the resulting triangle A'B'C'.

Let's calculate the length of a side of triangle ABC and the corresponding side of triangle A'B'C':

Length of side AB in triangle ABC:

AB = √(12 - 4)² + (4 - 4)²

= 8

Length of side A'B' in triangle A'B'C':

A'B' = √(3 - 1)² + (1 - 1)²

=2

To find the scale factor, we can divide the length of the corresponding side in the image triangle (A'B'C') by the length of the corresponding side in the original triangle (ABC):

Scale factor = A'B' / AB

= 2 / 8

= 1/4

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The point on the number line that has a value that is the opposite of 15 must be -15

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

Point = 15

The opposite of 15 is

Opposite = -15

This means that the point must have a value of -15

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Property of logarithms: The property of logarithms that we used in this problem states that if loga(b) ≥ loga(c), then b ≥ c. This property is true for any base of the logarithm. Note that the inequality symbol flips when you move from the logarithmic expression to the exponential expression.

Solving linear inequalities: To solve a linear inequality like ax + b > c, you need to isolate the variable on one side of the inequality. This involves adding or subtracting terms and possibly multiplying or dividing by constants. You need to be careful when multiplying or dividing by a negative number, as this flips the inequality symbol.

Domain restrictions: When solving logarithmic inequalities, you need to make sure that the argument of the logarithm is positive. This means that the expression inside the logarithm cannot be zero or negative. You need to check for domain restrictions and make sure that any values that make the argument zero or negative are not included in the solution.

Check the solution: After solving the inequality, it's always a good idea to check the solution to make sure that it satisfies the original inequality. You can plug in the solution to the inequality and make sure that both sides of the inequality are still true. If not, you may have made a mistake in solving the inequality.

To solve log2(7x-3) ≥ log2(x+12), you can start by using the fact that if loga(b) ≥ loga(c), then b ≥ c:

Using this property, you can rewrite the inequality as:

7x - 3 ≥ x + 12

Simplifying the inequality by subtracting x and adding 3 from both sides, you get:

6x ≥ 15

Dividing both sides of the inequality by 6, you get:

x ≥ 2.5

Therefore, the solution to the inequality is x ≥ 2.5 which is option C.

Note that when you use the property of logarithms to simplify an inequality, you need to make sure that the argument of the logarithm is positive. In this case, both arguments are positive as long as x > 3/7 and x > -12, respectively. However, these conditions are automatically satisfied when x ≥ 2.5, so there is no need to check them separately.

The sum of the measures of the interior angles of the pentagon is given as follows:

540º.

Hence the angle measures are given as follows:

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

A pentagon has five sides, that is, n = 5, hence the sum is given as follows:

S(5) = 180 x (5 - 2)

S(5) = 540º.

Then the value of x is obtained as follows:

x + 40 + 80 + x + 50 + x + 5 + 125 = 540

3x + 300 = 540

3x = 240

x = 80º.

Then the angle measures are given as follows:

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The total selling price, as per the percent rule, is $9,000.

You must first determine the selling price of each toy in order to determine the overall selling price.

As per the percent rule, the cost price plus the markup equals the selling price.

The cost price of each toy is $24, so the markup is 25% of $24, which is $6.

Therefore, the selling price of each toy is $24 + $6 = $30.

To find the total selling price, you need to multiply the selling price of each toy by the number of toys sold.

The store bought 300 toys, so the total selling price is 300 x $30 = $9,000.

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Answer:

Step-by-step explanation:

m=5/4

Answer:

15 5/8 - 15 4/5

= 15 25/40 - 15 32/40 (15-15 = 0)

= 25/40 - 32/40

= -7/40

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The volume of the oblique rectangular prism  is 629.1 unit² .

The length of the oblique rectangular prism = 6 unit

The width of the oblique rectangular prism = 9 unit

Using trigonometry the height will be

tan θ = perpendicular / base

Perpendicular = h

Base = 9

h/9 = tan (59)

h = 1.66 (9)

h = 11.6 unit

The height of the oblique rectangular prism = 11.6 unit  

The volume of the oblique rectangular prism = l × b ×h

The volume of the oblique rectangular prism = 6 × 9 ×11.6

The volume of the oblique rectangular prism = 629.1 unit²

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Answer: $4,580

Step-by-step explanation:

First, we need to calculate the monthly payment for the 15-year, fixed-rate loan at the original rate of 5.05%. We can use the formula for the monthly payment of a mortgage loan:

P = L[c(1 + c)^n]/[(1 + c)^n - 1],

where P is the monthly payment, L is the loan amount, c is the monthly interest rate (which is the annual interest rate divided by 12), and n is the total number of payments (which is the number of years multiplied by 12).

Plugging in the given values, we get:

L = $137,000

c = 0.0505/12 = 0.0042083 (rounded to 7 decimal places)

n = 15 x 12 = 180

P = $1,071.18

Next, we need to calculate the monthly payment at the lower rate of 4.81% if the buyers purchase four points. Each point costs 1% of the loan amount, so four points will cost 4% of the loan amount.

The new rate after purchasing four points is:

5.05% - 0.24% = 4.81%

The new loan amount after purchasing four points is:

$137,000 - (4% x $137,000) = $131,920

Using the same formula for the monthly payment, but with the new values for the loan amount and monthly interest rate, we get:

L = $131,920

c = 0.0481/12 = 0.0040083 (rounded to 7 decimal places)

n = 15 x 12 = 180

P = $1,030.98

The monthly savings due to the lower interest rate is:

$1,071.18 - $1,030.98 = $40.20

To calculate the cost of the four points, we need to divide the upfront cost of the points by the monthly savings:

Cost of four points = ($40.20 x 180)/0.0024 = $3,015

Therefore, the cost of the four points is $3,015, which is closest to $4,580.

The four points that the homebuyers are purchasing to lower their rate from 5.05% to 4.81% will cost them D. $5,480.

The points purchased for loans are charges that the borrower pays upfront to lower their interest rates.

Each point equals a percentage of the loan amount.

For example, four points on a $137,000 loan are 4 percent of the loan amount, or $5,480.

The loan amount for the purchase of the condominium = $137,000

Fixed interest rate = 5.05%

Loan period = 15 years

Loan option rate = 4.81%

Hence, Four points =  $137,000 x 4%

                              = $5,480

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