For the arithmetic sequence beginning with the terms {7, 11, 15, 19, 23 ...}, what is the sum of the first 31 terms?

a.)
1827

b.)
1950

c.)
2077

d.)
2208

Using proportions, considering the given ratio, it is found that 9090 grapes were there.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The ratio of bananas to grapes of 3:101 means that out of 104 fruits, 3 are bananas and 101 are grapes. Hence the rule of three is given as follows:

3 bananas - 101 grapes

270 bananas - n grapes.

Applying cross multiplication:

3n = 101 x 270

n = 101 x 270/3

n = 9090.

9090 grapes were there.

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The sine is defined as the ratio of the length of the opposite leg and the hypotenuse. Since the hypotenuse is the longest side, the numerator will be less than the denominator, and thus the fraction will be less than 1.

Answer:

The sine is defined as the ratio of the length of the opposite leg and the hypotenuse. Since the hypotenuse is the longest side, the numerator will be less than the denominator, and thus the fraction will be less than 1.

Step-by-step explanation:

The amount Cindy should increase in each dimension of the scaled model is 12 m.  

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape. It is also called a cuboid.

We have:

The scaled model of the container has dimensions 2m by 4m by 6m.

Volume of the scaled model = 2×4×6 = 48 cubic m

Let x be the amount by which each dimension is increased.

(2 + x)(4 + x)(6 + x) = 84(48)

[tex]\rm 48+44x+12x^2+x^3=4032[/tex]

[tex]\rm x^3+12x^2+44x-3984=0[/tex]

[tex]\rm x-12=0\quad \mathrm{or}\quad \:x^2+24x+332=0[/tex]

The quadratic equation has no real solution so,

x = 12 m

Thus, the amount Cindy should increase in each dimension of the scaled model is 12 m.  

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Using the z-distribution, the sample sizes are given as follows:

a) 822.

b) 1068.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

Item a:

The estimate is of [tex]\pi = 0.26[/tex], hence we solve for n when M = 0.03.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2[/tex]

n = 821.2

Rounding up, a sample of 822 is needed.

Item b:

No prior estimate, hence [tex]\pi = 0.5[/tex].

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]

n = 1067.11

Rounding up, a sample of 1068 is needed.

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The sum of the vectors given is -i

Vectors consists of y and x axis. They are plotted on an xy plane known as the argand diagram.

Given the following vectors

u = 3i - 8j

v = -4i + 8j

Take the sum of the vectors

u + v = (3i - 8j) + (-4i + 8j)

Take the sum to have

u + v = (3i-4i)+(-8j+8j)

u + v = -I

Hence the sum of the vectors given is -i

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Answer:

A) [tex]\frac{15}{8}[/tex]

Step-by-step explanation:

remember Soh Cah Toa!!

[tex]sin=\frac{opposite}{hypotenuse}\\ cos=\frac{adjacent}{hypotenuse} \\tan=\frac{opposite}{adjacent} \\\\cos=\frac{8}{17}\\\\a^2+b^2=c^2\\8^2+b^2=17^2\\64+b^2=289\\b^2=225\\\sqrt{b^2} =\sqrt{225}\\b=15=opposite\\\\tan=\frac{15}{8}[/tex]

The value of angle x is 127 degrees.

The angle x can be found as follows:

Angle on a straight line is 180 degrees.

Therefore, the sum of 53 degrees and x degrees is 180 degrees.

Therefore,

53 + x = 180°(sum of angles on a straight line)

subtract 53 from both sides of the equation

53 - 53 + x = 180 - 53

x = 127°

Therefore, the angle of x is 127 degrees.

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The probability that the team will win the sport is 77%.

Given that an area kicker in pro football incorporates a 77% probability of creating a field goal over 40 yards and every attempt field goal is independent.

Probability is how something is likely to happen. The probability of a happening is calculated by the probability formula by simply dividing the favorable number of outcomes by the overall number of possible outcomes.

So, his team will win the sport if he makes a goal otherwise loses.

Therefore, the Probability that his team will win the sport P[E] =P[making a field goal]

P[E]=77%

Hence, the probability that the team will win the sport when making a field goal is 77%.

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The expected value after 10 game at a carnival is 16.1 tickets.

Given the probabilities that bag lands into the outer ring, middle ring, center are 0.64, 0.11 and remaining. 1 ticket awarded for the outer, 2 for middle and 3 for middle.

We have to find the expected value we will get if we play the game 10 times.

Probability is the chance of happening an event among all the events possible. Value of probability lies between 0 and 1. The formula of probability is as under:

Probability=number of items/ total items in consideration.

Probability that bag lands in center is 1-0.64-0.11=0.25.

Expected value when game is played 1 time=1*0.64+2*0.11+3*0.25

=0.64+0.22+0.75

=1.61

Expected value when the game is played 10 times=10*1.61

=16.1 tickets.

Hence the expected value when game is played 10 times is 16.1 tickets.

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The true statement that explains the correlation coefficient is: C. As the baby gains weight, the prices of smartphone tend to increase.

The value of the correlation coefficient shows a relationship between two variables. A positive value suggests a positive relationship, meaning as one variable increases, the other also increases.

A correlation coefficient of  0.87 suggests a positive relationship between baby's weight and the price of smartphone, therefore, the true statement is:

C. As the baby gains weight, the prices of smartphone tend to increase.

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The amount that Mr Rogers would receive per annum is K 30,000.

The amount of money that Mr Rogers would receive per annum is a function of the worth of the bond bought and the interest rate.

Interest=   bond value x interest rate

0.15 x 200,000 = $30,000

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Answer:

(a) 1

(b) 1/2

(c) 1/2

Step-by-step explanation:

[tex]x^2 + y^2 = 5/8 (1)\\\frac{4}{3}xy = \frac{1}{4} (2)\\\\\textrm {From (2) by multiplying both sides by 3/4 we get}\\\\xy = \frac{3}{16} (3)\\\textrm{We know that } (x + y)^2 = x^2 + 2xy + y^2 \\\textrm{Adding 2xy to the LHS and RHS of equation 1 gisues us }\\x^2 + y^2 + 2xy = \frac{5}{8} + 2 * \frac{3}{16} = \frac{5}{8} + \frac{3}{8} = \frac{8}{8} = 1[/tex]

[tex](x + y)^2 = 1 == > x+y = \sqrt{1} = 1\\\\(x - y)^2 = x^2 -2xy + y^2\\\\\textrm{Subtracting 2xy from both sides of Equation 1}\\x^2 + y^2 - 2xy = \frac{5}{8} - 2*\frac{3}{16} = \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} \\x-y = \sqrt{\frac{1}{4}} = \frac{1}{2}\\\\x^2 - y^2 = (x+y)(x-y) = 1 . \frac{1}{2} = \frac{1}{2}[/tex]

The measure of side c if a is 5 cm and b is 9 cm in a right triangle is √106 cms.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

The measure of side c if a is 5 cm and b is 9 cm in a right triangle will be,

c² = 5² + 9²

c = √106 cms

Hence, the measure of side c if a is 5 cm and b is 9 cm in a right triangle is √106 cms.

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Answer:

The order of operations is Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

Step-by-step explanation:

The order of operations is PEMDAS.

P: Parenthesis

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

An easy way to remember PEMDAS is, please excuse my dear aunt sally.

Hope this helps!

If not, I am sorry.

Answer: 8.2

Step-by-step explanation:

As angles in a triangle add to 180 degrees,

[tex]\angle A=180^{\circ}-121^{\circ}-31^{\circ}=28^{\circ}[/tex]

So, by the Law of Sines,

[tex]\frac{a}{\sin A}=\frac{b}{\sin B}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{9 \sin 28^{\circ}}{\sin 31^{\circ}}\\\\a \approx \boxed{8.2}[/tex]

Observe that

[tex]x^2 + 3x + 1 = (x^2 + 4x + 4) - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - (x + 2) - 1[/tex]

so that

[tex]P(x+2) = (x+2)^2 - (x+2) - 1 \implies P(x) = x^2 - x - 1[/tex]

Then

[tex]P(x - 1) = (x-1)^2 - (x-1) - 1 \\\\ ~~~~~~~~ = (x^2 - 2x + 1) - (x - 1) - 1 \\\\ ~~~~~~~~ = \boxed{x^2 - 3x + 1}[/tex]

Alternatively, we can avoid find [tex]P(x)[/tex] altogether and instead first write [tex]x-1[/tex] in terms of [tex]x+2[/tex] :

[tex]x - 1 = (x - 1) + 2 - 2 = (x + 2) - 1 - 2 = (x + 2) - 3[/tex]

Then

[tex]P(x - 1) = P((x + 2) - 3) \\\\ ~~~~~~~~ = (x - 3)^2 + 3 (x - 3) + 1 \\\\ ~~~~~~~~ = x^2 - 3x + 1[/tex]

A characteristic of a simple random sample is that all samples of the same population have an equal chance to be selected.

A subset of a statistical population called a simple random sample is one in which each member has the same chance of being picked or selected.

A subset of participants is chosen at random by the researcher using this sampling approach from a population.

To make sure that the sample represents the population, simple random sampling is often performed and this technique helps to sample bigger populations more frequently than smaller subpopulations.

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Answer: f(x+3), f(x+2), f(x), f(x-1/2), f(x-4), f(x-7)

Step-by-step explanation:

For y=f(x-a), the vertex is shifted a units to the right.

So, to order from left to right, we need to order them so that the value of a increases from the least to the most.

Answer:

Range and median

Step-by-step explanation:

Range = 9 - 3 = 6

Median = 6

Mode = 9

Answer:

Fred scored 100
Bob scored 50
Gladys scored 20

Step-by-step explanation:

Fred = 50% * 200
        = 50/100 * 200
        = 0.5 * 200
        = 100

Bob  = 25% * 200
        = 25/100 * 200
        = 0.25 * 200
        = 50

Gladys = 10% * 200
            = 10/100 * 200
            = 0.1 * 200
            = 20

Answer:

<PQR is 130 degrees

Step-by-step explanation:

When it says the line bisects the angle, that means the two smaller angles are equal to each other.

Therefore 3x+5 = 2x+25

Now rearrange to get x.

3x-2x=25-5

x=20

Now plug the x back into both phrases and them together to get the final answer for <PQR.

20 * 3 + 5 = 65

20 * 2 + 25 = 65

65*2 = 130

Based on the calculations, the area of this triangle is equal to: A. Area = 1/2 × [√(x₂² + y₂²) × √(x₁² + x₁²)].

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

Next, we would find the distance between points A and B:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

AB = √[(x₂ - 0)² + (y₂ - 0)²]

AB = √(x₂² + y₂²)

Also, we would find the distance between points A and C:

Distance = √[(x₁ - x₂)² + (y₁ - y₂)²]

AC = √[(x₁ - 0)² + (y₁ - y0)²]

AC = √(x₁² + x₁²).

Now, we can find the area of this triangle:

Area = 1/2 × b × h

Area = 1/2 × AB × AC

Area = 1/2 × [√(x₂² + y₂²) × √(x₁² + x₁²)]

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Answer: B. 1/2√(x2^2 - x1^2) ( y2^2 - y1^2

Step-by-step explanation: Edmentum

The equation of the inverse function is given as n(t) = (t+3)/4

Given the function that is represented as;

[tex]t(n)=8\cdot\frac{n+3}{2}[/tex]

This is further simplified to have:

t(n) = 4(n + 3)

Replace t with t(n)

t = 4n - 3

Make n the subject of the formula

4n = t+3

n = (t+3)/4

Hence the equation of the inverse function is given as n(t) = (t+3)/4

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Answer:

The side of the square can be 13 or 9

Step-by-step explanation:

Let x equal the unknown side of the rectangle and y equal the side of the square. The given information is that the area of the square is 4cm^2 larger than that of the rectangle. Mathematically this can be represented as

[tex]11x+4=y^2[/tex]

The second known is that their perimeters are equal so,

[tex]22+2x=4y[/tex]

Solve the first equation in terms of x and substitute it into the second and you get the quadratic

[tex]y^2-22y+117=0[/tex]

[tex](y-13)(y-9)=0[/tex]

Therefore your side length for the square can be either of those.

The fraction of the course that are male is 1/4

The given parameter is:

Female = 3 * Male

As a fraction, we have:

Female + Male = 1

Substitute Female = 3 * Male in the above equation

3 * Male + Male = 1

This gives

4 * Male = 1

Divide by 4

Male = 1/4

Hence, the fraction of the course that are male is 1/4

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Answer:

1

Step-by-step explanation:

1 is ans p²=h²-b²

solved

In analyzing Manda’s work, she made a mistake instep 3, she did not subtract one x from the left side.

Fractions are known to be the parts of a complete or whole numbers of objects. It is known to have a numerator and a denominator and when solving for it, the rule of BODMAS must be obeyed.

In step 3 we see that (image attached)  she did not subtract one x from the left side. The right thing to do is to use x to cancel out on the both side and that will make the answer to  be correct but she did not.

So her error is seen in step 3 and as such, option C is correct.

See full question in the image attached.

Options are

Analyze Manda’s work. Is she correct? If not, what was her mistake?

A. Yes, she is correct.

B. In step 2, she needed to multiply both sides by 10.

C. In step 3, she did not subtract one x from the left side.

D. In step 4, she did not simplify her fraction.

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1) ray

2) line

3) line segment

4) adjacent angles

5) vertical angles

Answer:

1) RAY

2) LINE

3) LINE SEGMENT

4) VERTICAL ANGLES

5) VERTICAL ANGLES