A ball is projected upward from the ground. Its distance in feet from the ground in t seconds is given by s left parenthesis t right parenthesis equals negative 16 t squared plus 126 t. At what times will the ball be 217 feet from the​ ground?

Answer:

-8: (-4, -3]

-7: (-3, -1]

(-5, -1]: (-5, -1]

(-4, -1]: (-4, -1]

[-3, 1]: [-3, 1]

(2, 1): (1, 2]

Answer:

Step-by-step explanation:

Since we know that x + 1 is a factor of f(x), we can use synthetic division to find the other factor and then solve for the remaining zeros.

We set up synthetic division as follows:

-1 | 1 -3 16 20

| -1 4 -20

|_____________

1 -4 20 0

The last row of the synthetic division gives us the coefficients of the quadratic factor, which is x^2 - 4x + 20. We can use the quadratic formula to find its roots:

x = (-(-4) ± sqrt((-4)^2 - 4(1)(20))) / (2(1))

= (4 ± sqrt(-64)) / 2

= 2 ± 2i√2

Therefore, the three zeros of f(x) are -1, 2 + 2i√2, and 2 - 2i√2.

Answer:

A. Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Step-by-step explanation:

See Venn diagram below

Answer:

  6 cm

Step-by-step explanation:

You want the height of a trapezium with bases 17 cm, 35 cm and area 156 cm².

The formula for the are of a trapezium is ...

  A = 1/2(b1 +b2)h

Filling in the given values, we have ...

  156 = 1/2(17 +35)h = 26h

  6 = h . . . . . . . . . . divide by 26

The height of the trapezium is 6 cm.

Answer:

6cm

Step-by-step explanation:

To find:-

Answer:-

We are here given that the area of the trapezium is 156cm² and two of the parallel sides are 17cm and 35cm .We are interested in finding out the height of the trapezium.

The area of the trapezium is given by the formula,

[tex]:\implies \sf Area =\dfrac{1}{2}\times (s_1+s_1)\times h \\[/tex]

where s1 and s2 are the || sides of the trapezium and h is the height of the trapezium.

Now on substituting the respective values in the given formula, we have;

[tex]:\implies \sf 156cm^2 =\dfrac{1}{2} (17cm+35cm)\times h \\[/tex]

[tex]:\implies \sf 156cm^2(2) = 52cm (h) \\[/tex]

[tex]:\implies \sf h =\dfrac{156(2)}{52} cm\\[/tex]

[tex]:\implies \sf \pink{ height = 6 cm }\\[/tex]

Hence the height of the trapezium is 6cm .

A replacement value is a value that can be substituted for a variable in an equation or expression in order to solve for that variable or simplify the expression.

An expression is a combination of numbers, variables, and/or operators that represents a mathematical relationship or calculation. An expression can be as simple as a single number or variable, or it can be more complex and involve multiple operations and variables.

A variable is a symbol or letter that represents a quantity or value that can change or vary in different contexts.

In the given question,

A replacement value is a value that can be substituted for a variable in an equation or expression in order to solve for that variable or simplify the expression.

For example, suppose you have the equation 2x + 3 = 7, and you want to solve for x.

To do so, you can use a replacement value.

You can subtract 3 from both sides of the equation to isolate the term with x, which gives you:

2x = 4

Now, you can divide both sides of the equation by 2 to solve for x:

x = 2

In this case, the replacement value was the number 2, which was substituted for the variable x in the equation in order to solve for x.

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The area of this triangle is 30 m².

Area is a surface measure, that is, it is the amount of space that a geometric figure occupies on a flat surface.

To calculate the area of a triangle, we can use the formula:

Area = (base x height) / 2

In the case of the given triangle, we can choose the measure of 5m as the base and the measure of 12m as the height, since the height forms a right angle with the base and is perpendicular to it.

So, we have:

Area = (b*h)/2

Area = (5m * 12m) / 2

Area = 30m²

Answer:

y=9/x  => proportional

y = x - 12 ==> non-proportional

h = 3d ==> proportional

f = 1/3 e = proportional

Step-by-step explanation:

A proportional equation is of the general form

y = kx (directly proportional) or

y = k/x  (inversely proportional)

k is known as the constant of proportionality

y = 9/x ==> k = 9  proportional
y = x - 12  cannot be expressed as y = kx or y = k/x

h = 3d ==> k = 3  proportional

f = 1/3 e ==> k = 1/3   proportional

Answer:

622.04

Step-by-step explanation:

579.99 x 7.25% = 42.049 or 42.05

579.99 + 42.05 = 622.04

The total cost of the camera with sales tax included is $622.04.

A sales tax is a government-imposed consumption tax levied upon that purchase of goods and services. A standard sales tax is assessed at the moment of sale, received by the shop, and paid to the government.

Now according to the question;

The Listed price of the camera is $579.99.

The sales tax rate is 7.25%,

[tex]7.25\% \ \text{of} \ \$579.99 = (7.25\times579.99)\div100[/tex]

Sales tax = $42.04

[tex]\text{Total cost of camera = Listed price + sales tax amount}[/tex]

                                 [tex]= \$579.99 + \$42.04[/tex]

[tex]\text{Total cost of camera} = \$622.04[/tex]

Therefore, the total cost of the camera with sales tax included is $622.04.

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[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}[/tex]

[tex]\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4[/tex]

According to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]

Coordinate geometry, also known as analytic geometry, is a branch of mathematics that deals with the study of geometric shapes using algebraic principles. It involves the use of coordinates to represent points, lines, curves, and other geometric figures on a plane or in space.

we need to know the coordinates of its foci, co-vertices, and the center. We can start by finding the center of the ellipse, which is the midpoint of the line segment joining the foci:

Center = ( (-8 + (-8))/2 , (14 + (-16))/2 ) = (-8,-1)

Next, we can find the distance between the foci, which is given by:

[tex]distance between foci = 2c = sqrt[(14 - (-16))^2 + (-8 - (-8))^2] = 30[/tex]

where c is the distance from the center to either focus.

We also know that the distance between the co-vertices is given by:

distance between co-vertices = 2a = |-16 - 0| = 16

where a is the distance from the center to either co-vertex.

Finally, we can use the standard form equation for an ellipse centered at the origin:

[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]

where b is the distance from the center to either vertex.

To find b, we can use the Pythagorean theorem:

[tex]b^2 = c^2 - a^2 \\b^2 = 30^2 - 16^2\\b^2 = 784\\b = 28[/tex]

Now we have all the information we need to write the equation of the ellipse:

[tex](x+8)^2/16^2 + (y+1)^2/28^2 = 1[/tex]

Therefore, according to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]

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Answer:

the question is incomplete, so I looked for similar questions:

There are 3 sandwiches, 4 drinks, and 2 desserts to choose from.

the answer = 3 x 4 x 2 = 24 possible combinations

Explanation:

for every sandwich that we choose, we have 4 options of drinks and 2 options of desserts = 1 x 4 x 2 = 8 different options per type of sandwich

since there are 3 types of sandwiches, the total options for lunch specials = 8 x 3 = 24

If the numbers are different, all we need to do is multiply them. E.g. if instead of 3 sandwiches there were 5 and 3 desserts instead of 2, the total combinations = 5 x 4 x 3 = 60.

For this question's answer, there are 2 x 5 = 10 lunch specials are possible.

The number of lunch specials possible are 10.

We can use combinations for this case,

Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total of

[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]

If the order matters, then each of those choice of k distinct items would be permuted k! times.

So, total number of choices in that case would be:

[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]

This is called permutation of k items chosen out of m items (all distinct).

We are given that;

Number of sandwiches=2

Number of drinks=5

Now,

To find the total number of lunch specials, we need to multiply the number of choices for sandwiches by the number of choices for drinks.

Number of sandwich choices = 2

Number of drink choices = 5

Total number of lunch specials = 2 x 5 = 10

Therefore, by combinations and permutations there are 10 possible lunch specials.

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a) As per the given budget, the amount of interval that would be better for the city is 95% confidence interval.

b) The interval that be worse for the planners is depends on sample size

c) They achieve an interval estimate that would better serve their planning needs is depends on margin of error

d) The number of days worth of data should they collect to have confidence of estimating the true mean to 30 days

To obtain a better estimate, the city can create a confidence interval, which is a range of values that is likely to contain the true population mean with a certain degree of confidence.

However, there are also some disadvantages to using a confidence interval. The interval estimate may be wider than a point estimate, which means that the budget planners may have to allocate a larger budget to account for the uncertainty in the estimate.

To achieve a better interval estimate, the city could increase the sample size or reduce the variability of the data. Increasing the sample size reduces the margin of error and increases the precision of the estimate.

Finally, to determine how many days' worth of data the city should collect to estimate the true mean with a certain degree of confidence, the city would need to consider the desired level of precision, the variability of the data, and the desired level of confidence.

Typically, a larger sample size will provide a more accurate estimate, but this also depends on the variability of the data. In general, a sample size of at least 30 is recommended for a reasonably accurate estimate.

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(a) The area under the standard normal curve to the left of 1.73 is 0.9582.

(b) The area under the standard normal curve to the left of -0.69 is 0.2454.

(c) The area under the standard normal curve to the right of 1.3 is 0.0968.

(d) The area under the standard normal curve to the right of -2.82 is 0.9974.

(e) The area under the standard normal curve between -2.22 and 0.52 is 0.6851.

(f) The area under the standard normal curve between -1 and 1 is 0.6826.

(g) The area under the standard normal curve between -4 and 4 is 0.9998.

(a) Using a standard normal table, the area under the standard normal curve to the left of 1.73 is 0.9582.

(b) Similarly, the area under the standard normal curve to the left of -0.69 is 0.2454.

(c) The area to the right of 1.3 is the same as the area to the left of -1.3. Using a standard normal table, this area is 0.0968.

(d) The area to the right of -2.82 is the same as the area to the left of 2.82. Using a standard normal table, this area is 0.9974.

(e) To find the area under the standard normal curve between -2.22 and 0.52, we need to find the area to the left of 0.52 and subtract the area to the left of -2.22. Using a standard normal table, we find that the area to the left of 0.52 is 0.6990 and the area to the left of -2.22 is 0.0139. Therefore, the area between -2.22 and 0.52 is 0.6990 - 0.0139 = 0.6851.

(f) To find the area under the standard normal curve between -1 and 1, we need to find the area to the left of 1 and subtract the area to the left of -1. Using a standard normal table, we find that the area to the left of 1 is 0.8413 and the area to the left of -1 is 0.1587. Therefore, the area between -1 and 1 is 0.8413 - 0.1587 = 0.6826.

(g) The area under the standard normal curve between -4 and 4 is the same as the area to the left of 4 minus the area to the left of -4. Using a standard normal table, we find that the area to the left of 4 is 0.9999 and the area to the left of -4 is 0.0001. Therefore, the area between -4 and 4 is 0.9999 - 0.0001 = 0.9998.

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Using differentiation, the area of the triangle is decreasing at the given time.

The formula for the area of a triangle is:

A = (1/2)bh

where b is the base and h is the height.

Differentiating both sides of the equation with respect to time t, we get:

[tex]\frac{dA}{dt} = (1/2)[(\frac{db}{dt}) h + b(\frac{dh}{dt}) ][/tex]

Substituting the given values, we get:

[tex]\frac{dA}{dt} = (1/2)[(1)(10) + (5)(-2.5)] = (1/2)(10 - 12.5) = -1.25[/tex]

Since the derivative of the area with respect to time is negative (-1.25), the area of the triangle is decreasing at the given instant.

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The second decile of the given data set, "24, 64, 25, 40, 45, 34, 14, 26, 28, 24, 58, 51"  is 24.

To find the second decile of a data set, we first need to arrange the data in order from lowest to highest, that is :

⇒ 14, 24, 24, 25, 26, 28, 34, 40, 45, 51, 58, 64

The second decile represents the value that divides the data into two parts, where 20% of the data is below the value and 80% of the data is above the value.

Since there are 12 data points in this set,

So, 20% of the data is equal to 0.2 × 12 = 2.4.

Since we cannot have a fractional data point, we round up to 3.

So, the second decile is the third value in the ordered data set.

which is 24.

Therefore, The second decile is 24.

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Answer: Factors of 24 include: 1 and 24, 2 and 12, 3 and 8, 4 and 6

Step-by-step explanation:

The diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.

A common example of a random experiment is rolling a regular six-sided die. For this action, all possible outcomes/sample space can be specified, but the actual result on any given experimental trial cannot be determined with certainty.

Martin features a spinner with four compartments marked A, B, C, and D.

To get the correct result of the filling, first take the value of the horizontal bar and write the value from the corresponding vertical bar where both column are meeting.

Thus, the diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.

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The midpoint of a line or arc can be found using straight edge-compass-construction method by drawing two perpendicular bisectors. The intersection of these bisectors is the midpoint.

To find the midpoint of a line segment, first draw a straight line passing through both endpoints of the segment using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the line segment. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the line segment. The intersection of these bisectors is the midpoint of the line segment.

To find the midpoint of an arc, first draw a chord that intersects the arc at two points using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the chord. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the chord. The intersection of these bisectors is the center of the circle that the arc belongs to. Draw a line from the center of the circle to the midpoint of the chord. This line will intersect the arc at its midpoint.

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--The question is incomplete, answering to the question below--

"find the midpoint of a line and arc using straight edge-compass-construction method"

Answer:

Through observation, a=2, b=1 or vice versa .

Step-by-step explanation:

If a=2 and b=1

a² +b²=?

2² +1² =4+1=5

a²+b²=5

Since the p-value (0.0803) exceeds the significance threshold (0.05), the null hypothesis cannot be ruled out.

The mean in mathematics is a measurement of a collection of numerical data's central tendency. It is determined by adding up all of the values in the set and dividing the result by the total number of values. This value is frequently referred to as the average value. The mean (or mathematical mean) is calculated as follows: (Sum of Values) / Mean (number of values)

given

The null hypothesis states that the mean number of units generated during the day and night shifts is the same. The contrary hypothesis (Ha) states that more units are created on average on the night shift than on the day shift.

"day" + "night"

Bravo! Night precedes day.

b. The following method can be used to calculate the test statistic:

t = sqrt(1/n night + 1/n day) * sqrt(x night - x day)

where s p is the pooled standard deviation and x night and x day are the sample averages, n night and n day are the sample sizes, and s p is represented by:

Sqrt(((n night - 1)*s night2 + (n day - 1)*s day2) / (n night + n day - 2)) yields the value s p.

S p is equal to sqrt(((74 - 1)*35 + (68 - 1)*28) / (74 + 68 - 2)), which equals 31.88.

t = (358 - 352) / (31.88 * sqrt(1/74 + 1/68)) = 1.19

1.19 is the test result.

the p-value is 0.0803 as a result (rounded to 4 decimal places).

Since the p-value (0.0803) exceeds the significance threshold (0.05), the null hypothesis cannot be ruled out.

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The complete question is :- Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift than on the day shift. The mean number of units produced by a sample of 68 day-shift workers was 352. The mean number of units produced by a sample of 74 night-shift workers was 358. Assume the population standard deviation of the number of units produced is 28 on the day shift and 35 on the night shift.

Using the 0.05 significance level, is the number of units produced on the night shift larger?

a. State the null and alternate hypotheses.

O : Day/Night: H:

Day Night

b. Compute the test statistic. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

c. Compute the p-value. (Round your answer to 4 decimal places.) p-value

Answer:

center: (0, -2)

radius: 6

Step-by-step explanation:

You have to "complete the square" this allows you to fold up the expressions and put the equation in a standard kinda of format where you can pick the center and radius right out of the equation.

see image.

(a) Therefore after t = 1.75 seconds the diver will hit the water.

(b) The velocity the diver hit the water is 56 ft/s.

From the given condition we have d(t) = 16t²

and the height is 49ft

(a) Now when the diver hit the water the equation become

16t² = 49

t² = 49/16

t = ±7/4

t = ±1.75

since time can not be negative so t = 1.75

Therefore after t = 1.75 seconds the diver will hit the water.

(b)

Now differentiating d(t) with respect to t we get

d'(t) = 32t

now putting t=7/4 we get

the velocity d'(7/4) = 32*7/4

d'(7/4) = 56ft/s

Therefore the velocity the diver hit the water is 56 ft/s.

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The complete question is :

A cliff diver plunges from a height of 49ft above the water surface. The distance the diver falls in t seconds is given by the function d(t)=16t²ft

(a) After how many seconds will the diver hit the water?

(b) With what velocity (in ft/s ) does the diver hit the water?

Answer:

the answer is 12/13 simplified

Step-by-step explanation:

simplified

Rhiannon arrived home approximately 17 minutes earlier than Alexander.

This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

To solve this problem, we can use the formula:

time = distance / speed

a) The time it took Alexander to get home is:

time_Alexander = 14 km / 20 km/h = 0.7 hours

The time it took Rhiannon to get home is:

time_Rhiannon = 10 km / 24 km/h = 0.41667 hours

Since Rhiannon's time is smaller than Alexander's, Rhiannon arrived home earlier.

b) The time difference between their arrivals is:

time_difference = time_Alexander - time_Rhiannon = 0.7 hours - 0.41667 hours = 0.28333 hours

To convert this to minutes, we can multiply by 60:

time_difference_in_minutes = 0.28333 hours x 60 minutes/hour ≈ 17 minutes

Therefore, Rhiannon arrived home approximately 17 minutes earlier than Alexander.

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The value of the constant c that makes the following function are c = 0.

Constant is a term used to describe a value that remains unchanged or fixed throughout a program or process. It can be a numeric value, a character value, a string, or a Boolean (true/false) value. Common examples of constants include physical constants, mathematical constants, and programming-language keywords.A constant is a value that does not change, regardless of the conditions or context in which it is used. Common examples of constants include mathematical values such as pi (3.14159), physical constants such as the speed of light (299,792,458 m/s), and other constants such as the universal gravitational constant (6.67408 × 10−11 m3 kg−1 s−2).

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Therefore, c must equal 0 in order for the two sides of the function to be equal. and The one with the greater absolute value is b = 10.

A function is a block of code that performs a specific task. It is a subprogram or a set of instructions that can be used multiple times in a program.

27. For the function to be continuous at x = 7, the limit of the function as x approaches 7 from the left must equal the limit of the function as x approaches 7 from the right.
This means that the value of y as x approaches 7 must be the same on both the left and right sides of the point.
Since the left side of the function is y = c*y + 3, the right side of the function must also be equal to y = c*y + 3.
Therefore, c must equal 0 in order for the two sides of the function to be equal.

28. In order for the function to be continuous at x = 5, the value of y at x = 5 must be the same on both the left and right sides of the point.
Since the left side of the function is y = b - 2x, the right side of the function must also be equal to y = b - 2x.
Therefore, b must equal 10 in order for the two sides of the function to be equal.

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Complete Question:

Answer:

The square root of 20 is approximately between 4 and 5.

To find this, you can estimate the square root of 20 by finding the square root of the closest perfect squares, which are 16 (4^2) and 25 (5^2):

√16 = 4

√25 = 5

Since 20 is closer to 25 than 16, we know that the square root of 20 must be closer to 5 than to 4. Therefore, the square root of 20 lies between 4 and 5.

Here using the correct order of operations that is PEMDAS, we get the value to be 13.

PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.

The letters stand for:

P stands for parentheses.

Exponents are shown as E.

D stands for division.

The letter M stands for multiplication.

A stand for addition.

S stands for subtraction.

Now in the given question,

15 - (4-3)2

First the parentheses

15 - (1)2

Next is exponents.

15 - 2

At last, after subtracting, we get:

13

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