The following is a WFF:
(S~T) V (~U.W)
Select one:
True or
False

Uncle Harry rented 4 games, and using  that he also rented 8 movies.Therefore, the Lupine family has 8 horror movies and 4 gory games for their vacation.

What is word problem?

A word problem is a type of mathematical problem that is presented using words instead of or in addition to mathematical symbols and equations. Word problems often describe a real-world scenario or situation, and they require the solver to use math skills and critical thinking to identify the relevant information, determine the mathematical operation or operations required, and arrive at a solution to the problem.

Let's assume that the number of movies Uncle Harry rented is "m" and the number of games is "g". We want to find the values of "m" and "g".

From the problem statement, we know that:

The total number of movies and games rented is 12: m + g = 12

The cost of each movie is $3.99: 3.99m

The cost of each game is $4.50: 4.5g

The total cost before tax is $49.92: 3.99m + 4.5g = 49.92

We can use the first equation to express "m" in terms of "g":

m = 12 - g

Substituting this expression for "m" in the second equation, we get:

3.99(12 - g) + 4.5g = 49.92

Expanding the brackets and simplifying, we get:

47.88 - 3.99g + 4.5g = 49.92

0.51g = 2.04

g = 4

So Uncle Harry rented 4 games, and using the first equation, we find that he also rented 8 movies.

Therefore, the Lupine family has 8 horror movies and 4 gory games for their vacation.

Learn more about word problem click here:

https://brainly.com/question/25693822

#SPJ1

The radius of the circle is 2.8feet (nearest tenth)

Arc length is the distance between two points along a section of a curve.

The length of an arc is expressed as ;

L = (tetha) / 360 × 2πr

L is the length of the arc

tetha is the angle made by the two radii and the arc.

In radian 360° = 2π

therefore ;

8 = 2.9/ 2π × 2πr

8 = 2.9 r

r = 8/2.9

r = 2.76 ft

therefore the radius of the circle is 2.8 feet( nearest tenth) .

learn more about length of an arc from

https://brainly.com/question/2005046

#SPJ1

The number of possible combinations are 12.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.

Given that, Esther can choose a 2 or 4 door car with leather or cloth interiors in black, silver, or white.

Now, C(3, 1)×C(2, 1)×C(2, 1)

= 3×2×2

= 12

Therefore, the number of possible combinations are 12.

To learn more about the permutation and combination visit:

https://brainly.com/question/28065038.

#SPJ9

"Your question is incomplete, probably the complete question/missing part is:"

When buying a car, Esther can choose a 2 or 4 door car with leather or cloth interiors in black, silver, or white. How many possible combinations of her car selection?

This linear model's rate of change is 0.7 minute per song. This may be computed by subtracting the y-values (166.6 - 96.6) from the x-values (238 - 138).

A continual dependent variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behavior of complicated systems, as well as analysing scientific, economic, and medical data. Linear regression is a statistical technique for developing a linear equation. Linear functions have a straight line as their graph. There is one independent variable and one dependent variable in a linear function. x is the independent factor, while y is the dependent variable.

A linear equation is so named because plotting the graph of a given linear model yields a straight line.

To know more about linear model, visit

brainly.com/question/29757372

#SPJ1

The number of persons that can use the room at the same time is 36.

The volume of the cuboid = length x width x height

The room is a cuboid.

Volume of the room = length x width x height

L = 10m, W = 6m, Height = 3m.

Volume = 10 x 6 x 3 = 180 cubic meter.

If each person takes 5 cubic meter of air space,

Then the total person who can occupy the room at the same time is 180/5 = 36.

A cuboid is a three-dimensional geometric shape that is bounded by six rectangular faces, where each face is a parallelogram. It is also known as a rectangular prism. The faces of a cuboid are called its base and lateral faces. The base of a cuboid is the top and bottom rectangular faces, while the lateral faces are the four rectangular faces that connect the base.

Cuboids have eight vertices or corners, where three edges meet, and 12 edges, which are the straight lines that connect the vertices. The length, width, and height of a cuboid are the dimensions of the three pairs of parallel sides of its rectangular faces, and these measurements are usually denoted by l, w, and h, respectively.

To learn more about Cuboid visit here:

brainly.com/question/29424737

#SPJ4

Step-by-step explanation:

the probability of getting (a, b), i.e. the first card is a and the second card is b is 2/3 by conditional probability.

The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is computed by dividing the likelihood of the earlier occurrence by the likelihood of the subsequent, or conditional, event.

This is where the independent event and dependent event notion is used. Consider a student who misses class twice each week, omitting Sunday. What are the possibilities that he will take a leave of absence on Saturday of the same week if it is known that he will be absent from school on Tuesday? It has been noted that situations where the outcome of one event influences the outcome of a subsequent event are termed as conditional probability

We can work this out directly from the definition of conditional probability,

[tex]P(G_1|G_2)=P(G_1nG_2)/(P(G_1)[/tex]

Exactly one of the three cards has sides, so

P(G1∩G2)=1/3

and P(G1)=1/2

THEN

the probability of getting (a, b), i.e. the first card is a and the second card is b IS = 1/3÷1/2 = 2/3

learn more about conditional probability,

https://brainly.com/question/30144287

#SPJ4

Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.

Answer:

The volume of a rectangular prism with length 25 cm and width 40 cm can be calculated as follows:

Volume = Length * Width * Height

Since the height is not given, we cannot calculate the exact volume.

Step-by-step explanation:

The average rate of change over the interval [3,4] is given as follows:

3.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The numeric values for the ends of the interval are given as follows:

Then the change in the output is of:

32 - 29 = 3.

The change in the input is of:

4 - 3 = 1.

Hence the rate is of:

r = 3/1

r = 3.

More can be learned about the average rate of change of a function at brainly.com/question/11627203

#SPJ1

Answer:

A

Step-by-step explanation:

A is correct because 3+4 = 7

B is incorrect because 9/3=3 ,not 3/9

There is no x in C

D is incorrect because 8×3=24

E is incorrect because 3-10= -7 (negative)

hope this helped :)

The probability of a player spinning the color green and then rolling an even number is 1/12.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Spinner:

= {red, purple, blue, green, white, orange}

Cube:

= {1, 2, 3, 4, 5, 6}

Now,

The sample space of spinning and rolling a cube.

= {red, purple, blue, green, white, orange} x {1, 2, 3, 4, 5, 6}

The number of outcomes.

= 6 x 6

= 36

Now,

The outcome of spinning a green and an even number.

= (green, 2), (green, 4), (green, 6)

Number of outcomes = 3

Now,

The probability of a player spinning the color green and then rolling an even number.

= 3/36

= 1/12

Thus,

The probability of a player spinning the color green and then rolling an even number is 1/12.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ9

Mr. Titus travels a total of 7476 miles annually between Charlotte, North Carolina, and New York City.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that twelve times a year, Mr. Titus makes the trip from Charlotte to New York City and back. Each round trip covers a total distance of 623 miles.

The total distance will be calculated as:-

Distance = 12 x 623

Distance = 7476 miles

Therefore, Mr. Titus' annual mileage between Charlotte, North Carolina, and New York City is 7476 miles.

To know more about an expression follow

https://brainly.com/question/28736515

#SPJ9

(a) The probability that all the student pilots successfully land the plane using the simulator is 43%

(b) The probability that none of the student pilots successfully lands the plane using the simulator is 0.0026%

(c) The probability that exactly eight of the student pilots successfully land the plane using the simulator is 30.1%

Probability is a measure of the likelihood of an event occurring.

(a) What is the probability that all the student pilots successfully land the plane using the simulator?

Probability of all pilots successfully landing

=> 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 = 0.43 or 43%

So, the probability that all the student pilots successfully land the plane using the simulator is 0.43 or 43%.

(b) What is the probability that none of the student pilots successfully land the plane using the simulator?

The probability of each pilot failing to land the plane is 0.20. We can use the multiplication rule again to calculate the probability of none of the pilots successfully landing the plane.

Probability of all pilots failing to land = 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 = 0.000026 or 0.0026%

So, the probability that none of the student pilots successfully land the plane using the simulator is 0.0026% or 0.000026.

(c) What is the probability that exactly eight of the student pilots successfully land the plane using the simulator?

where P(X=k) is the probability of k successes, n is the total number of trials, p is the probability of success in one trial, and nCk is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.

In this case, we have n=9, k=8, p=0.80, and (1-p)=0.20. So, the probability of exactly eight pilots successfully landing the plane is:

P(X=8) = 9C8 * 0.80^8 * 0.20^(9-8) = 0.301 or 30.1%

So, the probability that exactly eight of the student pilots successfully land the plane using the simulator is 0.301 or 30.1%.

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4

The pair of figures is similar by SSS

The complete question is added as an attachment

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

Triangles BDC and FGC

When the side lengths of the triangle are compared, we have:

Side lengths of FGC are 5/3 multiplied by the side lengths of BDC

This means that the triangles are similar

And the similarity statement is SSS

Read more about triangles at

https://brainly.com/question/14285697

#SPJ1

On solving the provided question, we can say that Amount of commission = Total sales value x Rate of commission = 3,200

aggregate attempting to calculate the time required, total number or quantity. The quantity at hand or under consideration is incredibly energetic. the overall result, importance, or import. Principal, interest, and a third accounting. amounts, amounting, and amounted are word forms. flexible noun The quantity of something is how much there is, how much you have, how much you require, or how much you obtain. He requires that sum of money to get by.

[tex]Amount of commission = 3,200\\Total sales value = 80,000//[/tex]

Rate of commission = 4% on sales

Amount of commission = Total sales value x Rate of commission

Amount of commission = 80,000 x 4%

Amount of commission = 3,200

To know more about amount visit :-

brainly.com/question/8082054

#SPJ1

1) The mean of the data is 4.45.

2) The mode of the data is 11.

3) The median of the data is 4.

The mean of the data is the ratio of the sum of the given data and the number of the count of the data.

The mode of the data is the number that is repeated maximum number of times. The median of the data is when the data is arranged in an increasing order then the middle most value will be the median of the data.

Given data is 6 11 5 11 4 0 2 0 1.

The mean of the data is,

Mean =  ( 6 + 11 + 5 + 11 + 4 + 0 + 2 + 0 + 1 ) / 9

Mena = 4.45

Mode = 11

Median:- 0,0,1,2,4,5,6,11,11

Median = 4

To know more about mean, mode, and median follow

https://brainly.com/question/29660457

#SPJ9

Gwen has £0.75 money left over, as per linear equation if a litre of cola costs £1.25.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation."

It is given that Gwen has a £5 note and a £2 coin.

Therefore, she has a total of £(5 + 2) = £7

A liter of cola costs £1.25.

Therefore, (7 ÷ 1.25) = 5.6

Therefore, Gwen can buy a total of 5 liters of cola.

Now, Gwen has left money of £[7 - (5 × 1.25)] = £0.75

To know more about linear equation

https://brainly.com/question/13395953

#SPJ4

Complete question is:

Gwen has a £5 note and a £2 coin

a litre of cola cost £1.25

gwen buys as many liter bottles of cola as she can

how much money will she have left over

Answer:

504

Step-by-step explanation:

2 to the power of 9 is 512 2 to the power of 3 is 8 so 512-8 is 504 (hope w this helps!)

Answer:

504

Step-by-step explanation:

2^9 = 512

2^3= 8

512-8=504

At least 174 participants for the clinical trial, with half of them assigned to the current drug group and half assigned to the new drug group.

To answer this question, we need to consider some statistical concepts. The event rate, or the percentage of patients who progress to cancer, is a key factor in this scenario. The current drug has an event rate of 28%, while the new drug is expected to reduce this further to 23%. We want to detect a difference between these two rates, which is 5 percentage points.

The power of a statistical test is the probability of detecting a true difference between two groups, given that such a difference exists. In this case, we want the power to be at least 80%, which means that we want to have an 80% chance of detecting a true difference of 5 percentage points between the current and new drugs.

To calculate the sample size needed for the clinical trial, we need to consider the expected event rates, the desired power, and the level of statistical significance. The level of significance is typically set at 5%, which means that we are willing to accept a 5% chance of making a type I error (i.e., rejecting the null hypothesis when it is actually true).

Assuming a two-sided test (i.e., testing for a difference in both directions), we can use a formula or an online calculator to determine the sample size. The formula is:

n = (Zα/2 + Zβ)² [p₁(1-p₁) + p₂(1-p₂)] / (p₁ - p₂)²

where n is the sample size, Zα/2 is the critical value of the standard normal distribution at the 2.5% level (for a two-sided test), Zβ is the critical value of the standard normal distribution at the desired power (in this case, 80%), p₁ is the event rate for the current drug (28%), p₂ is the event rate for the new drug (23%), and (p₁ - p₂) is the expected difference in event rates.

Plugging in the values, we get:

n = (1.96 + 0.84)² [(0.28)(0.72) + (0.23)(0.77)] / (0.28 - 0.23)²

n = 173.2

Rounding up to the nearest whole number, we get a sample size of 174 participants.

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4

On solving the provided question we can say that from the graphs,

y = f(x) = |x| and g(x) = |x-h| + k

Mathematicians use diagrams to logically bring facts or values ​​using visual representations or charts. A graph point usually reflects a contact between two or more things. Nodes or vertices and corner form a graph, which is a nonlinear data construction. We often glue knots together called vertices. This graph has vertices V=1, 2, 3, 5 and edges E=1, 2, 1, 3, 2, 4 and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) are graphical representations of expanding growth. Logarithmic graph in the format of a triangle 

from the graphs,

y = f(x) = |x|

y = f(x) + k

y = f(x+h)

g(x) = |x-h| + k

now, it will be

k>0 and h<0

To know more about graphs visit:

brainly.com/question/11950136

#SPJ1

the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13.

In a standard deck of 52 cards, there are four jacks and four 4s, for a total of 8 cards that are either a jack or a 4. The probability of selecting a jack or 4 can be found by dividing the number of favorable outcomes (8) by the total number of possible outcomes (52): P(jack or 4) = 8/52. This fraction can be reduced by dividing both the numerator and denominator by 4: P(jack or 4) = 2/13. Therefore, the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13. Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide range of fields, from gambling and sports to scientific research and data analysis. Understanding probability is important for making informed decisions, predicting outcomes, and assessing risks.

To learn more about probability click here

brainly.com/question/30034780

#SPJ4

[tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex] is the representation of system of equation x+5y=7, 7x-2y=3

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

The system of linear equations

-x + 5y = 7

7x - 2y = 3

can be represented in matrix form as:

[tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex]

The matrix on the left represents the coefficients of the variables x and y, and the matrix on the right represents the constants on the right-hand side of each equation.

The vector on the left contains the variables x and y, and the vector on the right contains the constants.

Hence, [tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex] is the representation of system of equation x+5y=7, 7x-2y=3

To learn more on Matrices click:

https://brainly.com/question/28180105

#SPJ1

Answer:a is 3:9 B is 6:9

Step-by-step explanation:

Answer:

there is no solution

Step-by-step explanation:

The values for the angle B and the side lengths of the right-angled triangle ABC are B = 41°, a = 9.6 , and b = 8.3 using the trigonometric ratios of sine and cosine of angle 49°.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle ABC, we shall calculate for the angle B and side lengths a and b as follows:

A + B + C = 180° {sum of interior angles of a triangle}

49° + B + 90° = 180°

B = 180° - 139°

B = 41°

sin49 = a/12.7 {opposite/hypotenuse}

a = 12.7 × sin49 {cross multiplication}

a = 9.5848

cos49 = b/12.7 {adjacent/hypotenuse}

b = 12.7 × cos49 {cross multiplication}

b = 8.3319

Therefore, the values for the angle B and the side lengths of the right-angled triangle ABC are B = 41°, a = 9.6 , and b = 8.3 using the trigonometric ratios of sine and cosine of angle 49°..

Know more about trigonometric ratios here: https://brainly.in/question/1165363

#SPJ1

The expression that shows an equivalent expression include the following:

1/4(14x - 8 + 6x) = 5x - 2.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we have the following mathematical expression:

1/4(14x - 8 + 6x)

By opening and expanding the bracket, we have the following mathematical expression:

1/4(14x - 8 + 6x) = 1/4(20x - 8)

1/4(20x - 8) = 5x - 2

Read more on expression here: brainly.com/question/25767785

#SPJ1

Sampling type which will yield a representative sample is stratified random sampling.

A representative sample is a subset of a population that seeks to accurately reflect the characteristics of the larger group. For example, a classroom of 30 students with 15 males and 15 females could generate a representative sample that might include six students: three males and three females.

This method uses stratified random sampling to help identify its components. Other methods can include random sampling and systematic sampling. A representative sample seeks to choose components that match with key characteristics in the entire population being examined.

Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members' shared attributes or characteristics, such as income or educational attainment.

To know more about sampling

https://brainly.com/question/11045407

#SPJ4