which number comes next in this series 5, 7, 11, 19, 35

All the zeros of the polynomial f(x) = x³ - 12x² + 39x - 28 will be 7, 1, and 4.

Given that:

f(x) = x³ - 12x² + 39x - 28

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

⇒ (x³ - 12x² + 39x - 28) / (x - 7)

⇒ x² - 5x + 4

⇒ x² - 4x - x + 4

⇒ x(x - 4) -1(x - 4)

⇒ (x - 4)(x - 1)

The other roots are given as,

(x - 1)(x - 4) = 0

x = 1, 4

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After 1 year, you have invested $977.28. The Option B

To find the total amount, we have to determine monthly investment required.

Let's represent monthly investment as M.

After 12 months of compounding, the final amount will be $1000. We will use formula for compound interest [tex]A = P(1 + r/n)^{nt}[/tex]

To solve for monthly investment (M), we rearrange the formula as follows: [tex]A = M * ((1 + r/n)^{nt} - 1) / (r/n)[/tex]

[tex]1000 = M * ((1 + 0.05/12)^{12*1} - 1) / (0.05/12)\\M = $1000 * (0.05/12) / ((1 + 0.05/12)^{12*1} - 1)\\M = $81.4408151 \\M = $81.44[/tex]

To get total amount invested after 1 year, we will multiply investment by 12 months:

= $81.44 * 12

= $977.28.

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The area of the shaded region ( sector ) rounded to the nearest hundredth is 38.47 cm².

A sector of a circle is simply part of a circle made up of an arc and two radii.

The area of a sector of a circle can be expressed as:

A = (θ/360º) × πr²

Where θ is the sector angle in degrees, and R is the radius of the circle.

From the diagram:

The sector angle θ = 90 degrees

Radius r = 7cm

Plug these values into the above formula and solve for the area.

Area = (θ/360º) × πr²

Area = (90/360º) × 3.14 × (7 cm)²

Area = (90/360º) × 3.14 × 49 cm²

Area = 38.465 cm²

Area = 38.47 cm²

Therefore, the area of the sector is 38.47 cm².

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Answer:

11:1

Step-by-step explanation:

Convert it into a fraction : 11 6/11

Multiply both the numerator and the denominator by 11 to get rid of the fraction part.

121/11

Simplify this by dividing both the numerator and the denominator by 11

11:1

To determine if lab 1 is reporting lower cholesterol levels, on average, than lab 2, a paired t-test for means should be used.

This is because the physician collected pairs of blood samples from each patient and wants to compare the means of the two labs' cholesterol level measurements. The paired t-test for means is appropriate for comparing the means of two related samples, in this case, the blood samples from each patient tested by lab 1 and lab 2.

A paired t-test for means should be used to determine if lab 1 is reporting lower cholesterol levels, on average, than lab 2. This test is appropriate because the data consists of paired samples from the same patients, and the goal is to compare the means of the differences between the two labs.

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Answer:

Justin is packing a container with books the dimension of each book are 8 in by 6 in by 2 in the dimensions of the container are 16 in by 12 in by 12 in all of the books in the container are rectangular prisms how many books can fit in the container if the books are packed so that there is no unused space in the container

For linear trigonometric equations involving only sine or cosine, there will be solutions if the constant term on the other side of the equation falls within the range of -1 to 1.

When solving linear trigonometric equations in terms of only sine or cosine, we can determine whether there will be solutions by considering the range of values that sine and cosine can take.

For sine (sin) and cosine (cos), their values range from -1 to 1. If the equation involves only sine or cosine and is linear, it means the variable is not squared or involved in any higher powers. In such cases, the equation will have solutions if the constant term on the other side of the equation is within the range of -1 to 1.

For example, if we have the equation sin(x) = 0.5, it will have solutions because 0.5 is within the range of -1 to 1. However, if we have the equation sin(x) = 2, it will not have any solutions because 2 is outside the range of -1 to 1.

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Answer:

we will use the cross multiplication method.

144 is 45%

(?). is 100%

so (144×100)/45 = 320

so there were total 320 costumers

Answer:

20cm.

Step-by-step explanation:

You have to add all the sides so 5+7+8=20 cm. I hope this helps!

Step-by-step explanation:

Perimeter is just the sum of the side lengths

(5 + 7 + 8) cm  = 20 cm

Option (A) Names of TV shows taped in New York are an example of qualitative data. Qualitative data is descriptive in nature and does not involve numerical values or measurements.

It deals with qualities or attributes that cannot be expressed numerically. In this case, the names of TV shows are characteristics that describe the nature of the data. Quantitative data, on the other hand, is numerical data that can be measured and expressed in numbers. A parameter is a measurable factor or variable that can be used to define a system, while statistics is a branch of mathematics that deals with data collection, analysis, and interpretation. In conclusion, since the names of TV shows are descriptive in nature and do not involve numerical values, they are an example of qualitative data.

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The equation 3+7+2=+2 is actually not true, but false.

The equation 3+7+2=+2 is actually not true, but false. This is because the sum of 3, 7, and 2 is 12, not 2.

In general, an equation is considered true if the expressions on both sides of the equal sign are equivalent in value. In this case, the expressions on the left-hand side (3+7+2) and the right-hand side (+2) are not equivalent, and therefore the equation is false.

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Answer:

Step-by-step explanation:

x + [tex]\frac{y}{3}[/tex] = 0         ------    ( 1 )

6x - 2y = 6     ------    ( 2 )

6x + 2y = 0    ----- ( 3 )

6x - 2y = 6    ------ ( 4 )

Adding ( 3 ) and ( 4 ) ; we get ,

12x = 6

x = 1/2

putting value of x in (3) , we get ,

3 + 2y = 0

2y = -3

x + 2y = (1/2) - 3

= - 5/2

By identifying and isolating this effect, ANOVA provides a powerful statistical tool for determining whether there are significant differences between the means of the treatment groups being studied.

The source of variance that is presumed to explain between treatments variance in ANOVA is the treatment effect.

This effect represents the differences between the means of the treatment groups being compared. It is the primary factor being studied in ANOVA, as it is used to determine whether there are significant differences between the means of the treatment groups.

In ANOVA, the between treatments variance is explained by the treatment effect, which represents the differences between the means of the treatment groups being compared. This effect is the primary factor being studied in ANOVA, as it is used to determine whether there are significant differences between the means of the treatment groups. By isolating this effect, ANOVA allows researchers to determine whether any observed differences between the treatment groups are statistically significant or merely due to chance.

The treatment effect is the source of variance presumed to explain between treatments variance in ANOVA. By identifying and isolating this effect, ANOVA provides a powerful statistical tool for determining whether there are significant differences between the means of the treatment groups being studied.

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The given exponential function will grow at 7.1%

We have to given that;

The exponential function is,

⇒ y = 25 (1.071)ˣ

Now, For identify whether the change represents growth or decay, and to determine the percentage rate of increase or decrease.

Since, We have,

⇒ y = 25 (1.071)ˣ

Here, The equation represents exponential growth because the growth factor is 1.071 which is greater than 1.

Since, The general form equation is:

⇒ y(x) = a(1 + r)ˣ

such that r is the growth percent.

Hence,

⇒ 1 + r = 1.071

⇒ r = 0.071 = 7.1%

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So the altitude of the pile is increasing at a rate of 8/(45π) feet per minute when the pile is 6 feet high.

Let's call the radius of the conical pile at any given time "r" and the altitude "h". We are given that the altitude is always twice the radius, so we can write:

h = 2r

We are also given that water is pouring from a chute into the pile at a rate of 8 cubic feet per minute. The volume of a cone is given by the formula V = (1/3)πr^2h, so the rate of change of the volume of the pile is:

dV/dt = (1/3)πr^2 dh/dt + (2/3)πrh^2 dr/dt

We want to find the rate at which the altitude is increasing, so we need to solve for dh/dt when h = 6. We can also find r when h = 6 by using the equation h = 2r:

6 = 2r

r = 3

Now we can substitute the values we know into the equation for dV/dt:

8 = (1/3)π(3^2) dh/dt + (2/3)π(3)(6)^2 dr/dt

Simplifying:

8 = 9π dh/dt + 72π dr/dt

We can use the fact that h = 2r to eliminate r from this equation. Taking the derivative of both sides with respect to time:

dh/dt = 2 dr/dt

Now we can substitute this into the equation for dV/dt:

8 = 9π (2 dr/dt) + 72π dr/dt

Simplifying:

8 = 90π dr/dt

Solving for dr/dt:

dr/dt = 8/(90π) = 4/(45π)

Finally, we can use the equation h = 2r to find dh/dt:

dh/dt = 2 dr/dt = 8/(45π)

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The volume of the cone is V = 193.8 inches³

Given data ,

Let the volume of the cone be represented as V

Now , the height of cone h = 5.9 inches

And , diameter of cone = 11.2 inches

So , radius of cone r = 5.6 inches

where , Volume of Cone = ( 1/3 ) πr²h

V = ( 1/3 ) ( 3.14 ) ( 5.6 )² ( 5.9 )

V = 193.8 inches³

Hence , the volume is V = 193.8 inches³

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A 4.2 earthquake's energy release is 10 times more than a 3.2 earthquake's energy release despite the 3.2 earthquake's amplitude being 10 times smaller.

Now, A 3.2- to 6.5-magnitude earthquake has a substantial difference in intensity.

In actuality, a 6.5 earthquake has a magnitude almost 1000 times greater than a 3.2 earthquake.

The Richter scale, which uses a logarithmic scale to assess earthquake intensity, is the reason behind this.

Since, the Richter scale uses a seismograph to estimate the amplitude of earthquake waves, it is a logarithmic equation.

Each unit increase on the Richter scale causes an exponential increase in the energy released by the earthquake, which is proportional to the amplitude of the earthquake waves.

For instance, a 4.2 earthquake's energy release is 10 times more than a 3.2 earthquake's energy release despite the 3.2 earthquake's amplitude being 10 times smaller.

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The coefficient used to assess the internal consistency of a measure typically refers to Cronbach's alpha coefficient.

The coefficient used to assess the internal consistency of a measure typically refers to Cronbach's alpha coefficient. This coefficient is a statistic that quantifies the internal consistency reliability of a scale or measure, specifically for measures with multiple items or indicators that are intended to measure the same underlying construct.

The coefficient ranges between 0 and 1, with higher values indicating greater internal consistency. Cronbach's alpha measures the extent to which the items in a scale or measure correlate with each other. It assesses how well the items are measuring the same underlying construct or concept.

In other words, the coefficient represents the proportion of variance in the observed scores that can be attributed to the true score, rather than measurement error or other extraneous factors. It indicates the degree to which the items in the measure are interrelated or consistent with each other, with higher values suggesting stronger internal consistency.

Researchers often use Cronbach's alpha to assess the reliability of scales in various fields, such as psychology, education, and social sciences, to ensure that the measure is measuring the construct consistently and accurately.

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Answer:

67 mph

Step-by-step explanation

A method you'd want to remember is r = d/t, or rate equals distance divided by time.

Since the Morris family drove 368.5 miles in 5.5 hours, you'd divide the distance by 5.5.

(368.5/5.5) = 67 miles per hour.

So their average rate is 67 miles per hour.

Taylor will pay $1.60 for the grapes and $1.49 for the oranges, totaling $3.09 for both.

To calculate the cost of the grapes, we multiply the weight (1/4 lb) by the cost per pound ($3.20):

Grapes cost = (1/4) lb * $3.20/lb = $0.80.

Similarly, to calculate the cost of the oranges, we multiply the weight (1/2 lb) by the cost per pound ($2.98):

Oranges cost = (1/2) lb * $2.98/lb = $1.49.

To find the total amount Taylor will pay for the grapes and oranges, we add the individual costs together:

Total cost = Grapes cost + Oranges cost = $0.80 + $1.49 = $2.29.

Therefore, Taylor will pay $1.60 for the grapes and $1.49 for the oranges, totaling $3.09 for both.

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There are 160 different combinations of 2 snacks and 1 drink that can be chosen if you can't pick the same snack twice.

What is the combination?

Combinations are a way to count the number of ways to choose a subset of objects from a larger set, where the order of the objects does not matter.

Since you can't pick the same snack twice, the first snack can be chosen in 5 ways, and the second snack can be chosen in 4 ways (since there are only 4 remaining choices after choosing the first snack). The drink can be chosen in 8 ways.

Using the multiplication principle of counting, the total number of different combinations of 2 snacks and 1 drink is:

5 × 4 × 8 = 160

Therefore, there are 160 different combinations of 2 snacks and 1 drink that can be chosen if you can't pick the same snack twice.

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Answer: g(x)=(x-4)^(2)-5

Step-by-step explanation:

No, Tyler is wrong.

Given that according to Tyler all parallelograms can be classified as trapezoids, the diagonals of all trapezoids must intersect at their midpoints.

A parallelogram is a quadrilateral in which the opposite sides are parallel and equal.

Parallelograms are classified into three main types: square, rectangle, and rhombus, and each of them has its own unique properties.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Tyler's comment on trapezoids is totally wrong, because no trapezoid is considering as a parallelogram.

However, a trapezoid has one pair of parallel sides, but to be a parallelogram it should have both pairs of sides equal and parallel like a rectangle.

Hence Tyler is wrong.

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The forces are pulling at right angles to each other by using pythagorean theorem

To determine if the forces are pulling at right angles to each other, we can use the Pythagorean theorem

In a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have a resultant force of 130 lb, which represents the hypotenuse of the right triangle.

The other two forces are 50 lb and 120 lb.

Using the Pythagorean theorem, we can calculate:

(50 lb)² + (120 lb)² = (130 lb)²

2500 lb² + 14400 lb²= 16900 lb²

16900 lb² = 16900 lb²

The equation is true, which means the forces satisfy the Pythagorean theorem.

Therefore, the forces are pulling at right angles to each other.

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The volume of the cone is 7225.66 m³ and the volume of the hemisphere is 209.44 cubic feet.

From the general formula of the volume of the cone,

Volume = πr²h

in the given case,

Radius (r) = 10 m

Height (h) = 23 m

Thus, Volume = π*10²*23

Volume = 7225.66 m³

The formula for the volume of a hemisphere is:

V = (2/3) * π * r³

where π is pi (approximately 3.14159), and r is the radius of the hemisphere.

Substituting the given value of r = 10 ft, we get:

V = (2/3) * π * (10 ft)³

= (2/3) * π * 1000 ft³

= (2/3) * 314.16 ft³

≈ 209.44 ft³

Therefore, the volume of the hemisphere is approximately 209.44 cubic feet.

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The value of the length f is 6. 7

To determine the value, we have to know the different trigonometric identities.

These trigonometric identities are enumerated as;

To determine the length of f

Let us use the tangent identity, we have that;

tan θ = opposite/adjacent

substitute the values, we have;

tan 24 = f/15

Multiply the values, we get;

f = 0. 4452(15)

multiply the values

f = 6. 7

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Answer:

I can tell you the steps to find the answer.

step.1 calculate total number of squares in the given figure.

step.2 calculate total number of shaded squares.

step.3 to calculate the probability of the given event we will use P(E) = favorable outcomes / total outcomes.

The triangles are similar by the SAS similarity statement

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

The triangles in this figure are

TUV and TCD

These triangles are similar is because:

The triangles have similar corresponding sides and congruent angles

By definition, the SAS similarity statement states that

"If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar"

This means that they are similar by the SAS similarity statement

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There are 6 possible outcomes when rolling a single standard six-sided number cube: 1, 2, 3, 4, 5, or 6. When rolling two number cubes, the possible sums range from 2 (1+1) to 12 (6+6).

To find the number of ways to roll a sum of 7, we need to look at all the possible combinations of numbers on the two cubes that add up to 7. These are: 1+6, 2+5, 3+4, 4+3, 5+2, and 6+1. Therefore, there are 6 ways to roll a sum of 7 when rolling two standard six-sided number cubes.

To determine how many ways Tre can roll a sum of 7 using two standard six-sided number cubes, we'll consider the possible outcomes:

1. First cube shows 1, second cube shows 6 (1+6=7)
2. First cube shows 2, second cube shows 5 (2+5=7)
3. First cube shows 3, second cube shows 4 (3+4=7)
4. First cube shows 4, second cube shows 3 (4+3=7)
5. First cube shows 5, second cube shows 2 (5+2=7)
6. First cube shows 6, second cube shows 1 (6+1=7)

There are 6 different ways Tre can roll a sum of 7 using two standard six-sided number cubes.

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Answer:

first one is 68,328

Step-by-step explanation:

because if one liter rounded to a gallon is 4 then you gotta multiply 94.9 times 4 then multiply that by 180 us gallons then theres your answer