In the Venn diagram in Fig. 8.8 the numbers of elements are as shown. P x - 16 X 4 -Q x - 11 -8- Fig. 8.8 Given that n(PUQ) = n(PUQ)', find x and hence find n(%).​

Step-by-step explanation:

Triangles' angles always sum to 180 °

A  Not possible    sum = 185°

B  Not possible    sum = 170°

C  YES    sum = 180°

D YES

E Not possible    sum = 175°

Answer:

Below

Step-by-step explanation:

Use trig identity :

 cos (x/2) = +- sqrt ((1+cos x)/2) = +- sqrt((1 + -2/3)/2)

          = +- sqrt (1/3 /2) =   +- sqrt (1/6)  

                since x is in Q II ,   x/2   is in   Q I  (where cos is positive )  the positive value is the one you need:   sqrt (1/6 )        ( or  sqrt (6) / 6   )

Charlie can spend 25 on each of the remaining gifts.

Germanic in origin, the gender-neutral name Charlie means "free man." It comes from the Germanic words kerle, which means "warrior," and karal, which means "free man." Charles is sometimes referred to as "Charlie" and the name has a number of lovely alternatives, including Charlotte. The United States frequently referred to them as the Viet Cong as a group. It was frequently abbreviated to VC, which was spoken as Victor Charlie in military alphabet code. That was condensed even more to Charlie. They went by the name Charlie and identified as liberators, according to US soldiers.

Based on the given conditions,

Formulate:

15+5*x=140

Rearrange the terms5x=140-15

Calculate.

5x=125

Divide the both sides.

x=125/5

Simplify.

x=25

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Step-by-step explanation:

we can make the coefficients of y equal by multiplying the first equation by 2:

y = 3x - 4 (multiply by 2)

2y = 6x - 8

Now we have:

2y = 6x - 8

2y = 2(3x - 4)

Next, we can subtract the second equation from the first equation to eliminate y:

2y - 2y = (6x - 8) - 2(3x - 4)

Simplifying the right side:

0 = 0

This equation is true for all values of x and y, which means that the two equations are equivalent and have infinitely many solutions.

Therefore, the solution set is all ordered pairs of the form (x, y) that satisfy the equation y = 3x - 4.

Answer:

m = 1/2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-2,3) (0,4)​

We see the y increase by 1, and the x increase by 2, so the slope is

m = 1/2

Answer:

The slope is [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

In order to find the slope of the line, we can use the formula [tex]\frac{y2-y1}{x2-x1}[/tex] where y2, y1, x2, and x1 are points on the line. We are given points on the table which allows us to plug in these values and evaluate.

Lets take two ordered pairs from the table:

(0,4) and (2,5)

Now we plug them into the formula.

[tex]\frac{5-4}{2-0}[/tex]

Evaluate

[tex]\frac{1}{2}[/tex]

The slope of the line is [tex]\frac{1}{2}[/tex]

Answer:

[tex]\dfrac{240}{4} =60[/tex]

[tex]\dfrac{1800}{3}=600[/tex]

Step-by-step explanation:

1.  The result should by a 2 digit number.

So, I fix a two digit number first, say 60.

Then, I multiplied it by some random integer, say 4 and got 240.

Now, 240 is my dividend and 4 is my divisor.

My division problem is:

[tex]\dfrac{240}{4} =60[/tex]

2.  The result should be a 3 digit number.

So, I fix a three digit number first, say 600.

Then, I multiplied it by some random integer, say 3 and got 1800.

Now, 1800 is my dividend and 3 is my divisor.

My division problem is:

[tex]\dfrac{1800}{3}=600[/tex]

Step-by-step explanation:

the first wound be the sum of a

15×9 rectangle and a 15×(15-9) triangle.

the area of a rectangle is

length × width.

the area of a triangle is

baseline × height / 2.

15×9 = 135 mm²

15×(15-9)/2 = 15×6/2 = 15×3 = 45 mm²

the total area is

135 + 45 = 180 mm²

for the second I have an even easier solution :

the area is

the area of the large 14×12 rectangle minus the inner, smaller 6×9 rectangle.

so,

14×12 = 168 m²

6×9 = 54 m²

so the total area is

168 - 54 = 114 m²

the third is simply a triangle, where we got the baseline (7), although it is on the top, but that is irrelevant. and we got the height (4).

so, as in the first example, the area of a triangle is

baseline × height / 2 = 7×4/2 = 7×2 = 14 units²

the fourth :

the area of a parallelogram is

baseline × height.

do not forget, the baseline to a height (or vice versa) is identified by a right angle between each other.

so, we have

16 × 15 = 240 units²

When Paolo and Roberta work together, they can mow the lawn in 6/5 hours, or 1 hour and 12 minutes.

A fraction, which is stated as one number divided by another, is a means to represent a portion of a whole or a quotient of two values. The denominator represents the entire or divisor, whereas the numerator represents the portion or quotient under consideration.

Contrarily, a ratio is a comparison of two amounts or measures that is stated as the quotient of two different integers. A ratio is not always simplified or represented in terms of a single unit, unlike a fraction.

Let us suppose time = t.

Thus,

1/2 + 1/3 = 1/t

Take the LCM we have:

3/6 + 2/6 = 1/t

5/6 = 1/t

t = 6/5

Therefore, when Paolo and Roberta work together, they can mow the lawn in 6/5 hours, or 1 hour and 12 minutes.

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After answering the given query, we can state that Therefore, the probability expected value of guessing is 0.2 points.

Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an occurrence will occur. The likelihood that an occurrence will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as numbers between 0 and 1. the proportion of equally probable choices that actually happen in comparison to all other outcomes when a specific event occurs.

a) Here is the decision tree for Dalton's random guess:

           /-- A (1 point)

          /

 Guess --|-- B (0 points)

          \

           \-- C (0 points)

           /-- D (0 points)

          /

 Guess --|-- E (0 points)

          \

           \-- F (0 points)

The branches on the left stand in for making a prediction that is accurate with a chance of 1/5 and receiving one point. The right-hand branches represent guessing wrong with a probability of 4/5 and receiving no points.

b) We multiply the value of each result by its probability and add up all of the outcomes to determine the expected value of guessing.

One point will be awarded if the estimate is accurate, which has a 1/5 chance of happening. The likelihood of making an incorrect estimate is 4/5, and the result is worth 0 points. Consequently, the expected value of a prediction is

(1/5) * 1 + (4/5) * 0 = 1/5

Therefore, the expected value of guessing is 0.2 points.

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The probability of selecting a yellow ball is approximately 37%.

P(yellow)=37%.

What is probability ?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. 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 many areas of mathematics, science, and everyday life to help us make decisions, assess risk, and understand uncertainty. It is an important concept in statistics, which uses probability to study and analyze data.

According to the question:

To find the probability of selecting a yellow ball, we need to divide the number of yellow balls by the total number of balls in the bag.

Total number of balls = 15 green + 18 yellow + 16 orange = 49

So, the probability of selecting a yellow ball is:

P(yellow) = Number of yellow balls / Total number of balls = 18/49

Rounding to the nearest percent, we get:

P(yellow) ≈ 37%

Therefore, the probability of selecting a yellow ball is approximately 37%.

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Answer:

A and D

Step-by-step explanation:

Answer:

A & D

Step-by-step explanation:

B. 2（6x + 1）= 12x + 2

C. 3（5x + 1）= 15x + 3

D. 6x + 2x + 4 - 1 = 8x + 3

The correct answer is (a) $234.95.

what is compund interest?

Compound interest is a type of interest where the interest is added to the principal amount of a loan or investment, and then the interest for the next period is calculated based on the new total. This means that the interest earned in each period is added to the original principal, and then interest is calculated on the new total for the next period.

ax + b = 0

where a and b are constants. The variable x appears only with the first power, and the coefficient a is not equal to zero.

Here's the explanation:

The school will pay 10% of the cost of the copy machine in cash, which is:

10% of $5,500 = 0.1 x $5,500 = $550

So the amount that needs to be financed through the credit union is:

$5,500 - $550 = $4,950

The credit union will charge 4% per year compounded monthly for 2 years. To calculate the monthly payment, we first need to calculate the total amount that will need to be paid back after 2 years, including interest. We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the total amount to be paid back

P = the principal amount (the amount borrowed)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time in years

In this case:

P = $4,950

r = 0.04 (4% as a decimal)

n = 12 (monthly compounding)

t = 2 (2 years)

Plugging in these values, we get:

A = $4,950(1 + 0.04/12)^(12*2) = $5,365.39

So the total amount that needs to be paid back is $5,365.39. To calculate the monthly payment, we can use the formula for a fixed-payment loan:

P = (rA)/(1 - (1+r)^(-n))

where:

P = the monthly payment

r = the monthly interest rate (as a decimal)

A = the total amount to be paid back

n = the number of payments (in this case, the number of months)

In this case:

r = 0.04/12 = 0.0033333 (monthly interest rate)

A = $5,365.39

n = 2*12 = 24 (2 years, with monthly payments)

Plugging in these values, we get:

P = (0.0033333 x $5,365.39)/(1 - (1 + 0.0033333)^(-24)) = $234.95

So the school's monthly payment will be $234.95. Therefore, the correct answer is (a).

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12112213213213211111111111111111111

Answer:

QPxMO is equal to QOMN

Step-by-step explanation:

Since we are given that angle QPO is congruent to angle MNO, we can conclude that triangle QPO is similar to triangle MNO.

Therefore, we can write:

QP / MN = PO / NO (corresponding sides of similar triangles)

Multiplying both sides by MN, we get:

QP = (PO / NO) * MN

Now, we can use this expression for QP to prove that QPxMO=QOMN:

QPxMO = QP + PO (by segment addition postulate)

QPxMO = [(PO / NO) * MN] + PO (substituting QP with (PO / NO) * MN)

QPxMO = PO * [(MN + NO) / NO] (factoring out PO)

QPxMO = PO * (MO / NO) (since MN + NO = MO)

Now, we can see that PO * (MO / NO) is the same as QOMN, which means:

QPxMO = QOMN

Therefore, we have proven that QPxMO is equal to QOMN.

Hope this helped, I'm sorry if it is wrong. If you need more help, ask me!
:]

Answer:

10.67 square inches

Step-by-step explanation:

Since the volume of the cube-shaped box is 64 cubic inches and each of the smaller cubes has an edge length of 1 inch, the number of smaller cubes needed to fill the box is 64.

Since the box is a cube, it has six equal faces. Since each face of the box is made up of smaller cubes with an edge length of 1 inch, the area of each face of the box is equal to the number of cubes that make up the face.

Therefore, the area of each face of the box is 64 divided by the number of faces, which is 6.

Area of each face = 64 / 6 = 10.67 square inches (rounded to two decimal places)

So, the area of each face of the box is approximately 10.67 square inches.

The perimeter of this figure is 61.27cm. A quarter circle and a rectangle make up this figure.

In the Euclidean plane, a rectangle is a rectangle with four right angles. A parallelogram with a right angle or an equiangular quadrilateral, where equiangular means that all of its angles are equal, are other ways to define it. A rectangle with four equally long sides is a square. A rectangle is an illustration of a quadrilateral having equal and parallel opposite sides. It is a polygon with 4 corners and four 90-degree angles. Since a square has rectangles with equal-length sides, it is a special kind of rectangle. Every square is also a rectangle since a square is a quadrilateral with all four angles at right angles.

P=20+2+(20-11)+11+3.14*11*2*1/4+2

P=20+2+9+11+17.2+2

=61.27cm

πr

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Answer:

154 cm²

Step-by-step explanation:

The diameter of the largest circle that can be drawn inside the square of 14 cm length = side of the square

Therefore diameter of circle = 14 cm

Hence area of circle = πr²

22/7 * 7 * 7

= 154 cm²

the equation for the function in vertex form is f(x) =[tex]\frac{1}{3}[/tex](x + 4)² - 7.

A quadratic function is a type of mathematical function that has the form:

f(x) = ax²+ bx + c

where x is the input or independent variable, f(x) is the output or dependent variable, and a, b, and c are constants, with a ≠ 0.

A quadratic function's vertex form is:

a(x - h)² + k = f(x)

where an is a constant that governs the parabola's form and (h, k) is the parabola's vertex.

Therefore, the equation for the function in vertex form is f(x) = [tex]\frac{1}{3}[/tex](x + 4)² - 7. The vertex of this parabola is (-4, -7), and the constant a is [tex]\frac{1}{3}[/tex].

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A quarter of 6 hours is 1.5 hours or 90 minutes, and 60 minutes is equivalent to 1 hour. Therefore, a quarter of 6 hours and 60 minutes is equivalent to 2.5 hours or 150 minutes.

A quarter is a unit of measurement that represents one-fourth or 25% of a whole. It is commonly used to divide time, money, and other quantities into equal parts. For example, a quarter of an hour is 15 minutes, and a quarter of a dollar is 25 cents. In terms of fractions, a quarter is equivalent to 1/4 or 0.25. The term "quarter" can also refer to a period of time, such as a school term or business quarter, which typically consists of three months or 13 weeks. The word "quarter" comes from the Latin word "quartus," which means fourth.

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Answer:

(-2,1)

Step-by-step explanation:

The solution is where in the graph, both lines intersect. In this case, both lines intersect at (-2,1), so the answer is (-2,1).

Answer: There are 11 marbles in the bag, so the total number of ways to draw two marbles without replacement is:

11C2 = (1110)/(21) = 55

Now, we need to find the number of ways to draw two marbles of different colors. There are three possibilities:

Green and yellow: There are 4 green marbles and 4 yellow marbles to choose from. The number of ways to choose one green and one yellow marble is:

4C1 * 4C1 = 4*4 = 16

Green and red: There are 4 green marbles and 3 red marbles to choose from. The number of ways to choose one green and one red marble is:

4C1 * 3C1 = 4*3 = 12

Yellow and red: There are 4 yellow marbles and 3 red marbles to choose from. The number of ways to choose one yellow and one red marble is:

4C1 * 3C1 = 4*3 = 12

So, the total number of ways to draw two marbles of different colors is:

16 + 12 + 12 = 40

Therefore, the probability of drawing two marbles of different colors is:

40/55 = 8/11

Answer: 8/11

Step-by-step explanation:

The right option is: If Olivia buys 12 spinning reels, she can buy 0 casting reels. This can be seen from the graph where the line connecting (0,10) and (12,0) represents all possible combinations of casting and spinning reels that Olivia can buy.

The graph shows the relationship between the number of casting reels and spinning reels that Olivia can buy with her expense account. The line represents all possible combinations of casting and spinning reels she can buy within her budget. If Olivia decides not to buy any spinning reels, she can buy 10 casting reels, which corresponds to the y-axis intercept of the line. This means that for every spinning reel she buys, she must give up some number of casting reels, as the line has a negative slope. In this case, for every 6 spinning reels purchased, she must give up 5 casting reels.

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Answer:

this is kinda hard I'm in grade 6bbtw im text so it can be 20

Answer:

x=0

Step-by-step explanation:

8(4x-4)=-5x-32

32x-32=-5x-32

32x=-5x

37x=0

x=0

You can get to 37x by adding 5x to both sides of the equation, shown on lines 3-4.

Check the picture below.

[tex]\sin(a)=\cfrac{\stackrel{opposite}{11}}{\underset{hypotenuse}{11.18}}\hspace{5em} \cos(a )=\cfrac{\stackrel{adjacent}{2}}{\underset{hypotenuse}{11.18}} \\\\\\ \tan(a )=\cfrac{\stackrel{opposite}{11}}{\underset{adjacent}{2}}\hspace{5em}\tan(b )=\cfrac{\stackrel{opposite}{2}}{\underset{adjacent}{11}}[/tex]

sinA: 11/11.18 or 0.9839

cosA: 9/11.18 or 0.8050

tanA: 11/9 or 1.2222

sinB: cosA

cosB: sinA

tanB: 9/11 or 0.8182

Answer:

Step-by-step explanation:

uuuum

An answer choice that matches the graph of the given piecewise-defined function include the following: D. graph D.

In Mathematics, a piecewise-defined function refers to a type of function that is defined by two or more mathematical expressions over a particular domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains.

When the domain is -2 < x ≤ -1, the rule for the piecewise-defined function f(x) is given by:

f(x) = -3

When the domain is -1 ≤ x ≤ 0, the rule for the piecewise-defined function f(x) is given by:

f(x) = -2

When the domain is 0 ≤ x ≤ 1, the rule for the piecewise-defined function f(x) is given by:

f(x) = -1

In conclusion, we can reasonably infer and logically deduce that all of the y-values of this piecewise-defined function are located on the negative y-coordinate based on the domain.

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The answer is either 0.2 as a decimal or 1/5 as a fraction.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.

To estimate the probability that Maria succeeds at fewer than 7 free-throws in a sample of 10, we need to sum up the number of successful free-throws in each simulated sample that are less than 7, and then divide by the total number of simulated samples.

From the dot plot, we can see that there are 5 simulated samples with fewer than 7 successful free-throws.

Therefore, the estimated probability that Maria succeeds at fewer than 7 free-throws in a sample of 10 is:

P(fewer than 7 successes) ≈ 5/25 ≈ 0.2

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