Can somebody please help me with this

The time taken to reaches its maximum height is 3s.

In the question,

It is given that,

Height, h(t) = \(96t - 16t^{2}\)

The maximum value of the function is obtained if the first derivative of the function h (t) = 0.

\(\frac{dh(t)}{dt} = 96 - 32t = 0\)

⇒ \(t = 3\)

So, time taken to reach its max height is 3 seconds.

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The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.

The formula for the surface area of a rectangular prism is given by:

Surface Area = 2*(length width + length height + width*height)

Initial Surface Area:

Length (L) = 13 cm

Width (W) = 8.7 cm

Height (H) = 28 cm

Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)

Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:

New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))

To find the increase in surface area, we subtract the initial surface area from the new surface area:

Increase in Surface Area = New Surface Area - Initial Surface Area

Let's calculate the values:

Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²

Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²

Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

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Tan(x/2) = (1 + cosx)/sinx is equivalent to the trigonometric identity cscx

An equation is an expression that can be used to show the relationship between variables and numbers.

Trigonometric identities are based on the six trigonometric ratios. They are sine, cosine, tangent, cosecant, secant, and cotangent.

It is given as:

tanФ = sinФ/cosФ, cotФ = 1/tanФ = cosФ/sinФ, cosecФ = 1/sinФ and secФ = 1/cosФ

According to half angle formula:

tan(x/2) = (1 + cosx)/sinx

Hence:

tan(x/2) + cotx = [(1 - cosx)/sinx] + (cosx/sinx)

tan(x/2) + cotx = (1 - cosx + cosx)/sinx

= 1/sinx

= cscx

Therefore tan(x/2) = (1 + cosx)/sinx is equivalent to cscx

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Answer:

Step-by-step explanation:

96 = 2w²

48 = w²

√48 = w

√(16)(3) = w

± 4√3  = w

± 6.93

w = 6.93, -6.93

The number on questions in part A were 3.

Here, we are given that Ms. Campbell wrote a test.

Part A had true/false questions, each worth 8 points.

Part B had multiple choice questions, each worth 6 points.

Let the number of questions in part A be x

and let the questions in part B be y

Then,

the total number of points in part A = 8x

and the total number of points in part B = 6y

Further, it is given that she made the number of points for Part A equal the number of points for Part B.

⇒ 8x = 6y

Now, we see that the Least Common Multiple of 8 and 6 is 24.

Thus, the least value of the total number of points can be 24.

⇒ 8x = 6y = 24

thus, x = 24/8 = 3

and y = 24/6 = 4

Thus, we get that the number on questions in part A were 3.

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The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping

Rewriting 125x^ 3 −27 as (5x) ^3 −3³

The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )

Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.

Hence, (5x−3)(25x ^2 +15x+9)

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Answer: A) 2 and a half B) 5 pints

Step-by-step explanation:

in 1 cup there are 16 table spoons.

a) 4tbsp (2 servings) times 10 (to reach 20 servings) =40 tbsp

40/16 =2.5

ANSWER A= 2 and a half cups of lemon juice.

in 1 pint there are 2 cups.

b)

1 cup = 1/2 a pint,

1/2 pint (2 servings) times 10 (to reach 20 servings) = 5 pints

ANSWER B= 5 pints of olive oil

Answer:is the secend one

Step-by-step explanation:this is easy you just have to find the points

Answer:

(2,5) (6,9) (7,2)

Step-by-step explanation:

the first number is the x and the second number is the y

The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.

The figures in the image are right triangles.

A)

angle D = 17 degree

Adjacent to angle D = 14 mm

Opposite to angle D = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( 17 ) = x/14

x = tan( 17 ) × 14

x = 4.3mm

B)

angle Z = 82 degree

Adjacent to angle Z = 43.1 m

Hypotenuse = x

Using trigonometric ratio,

cosine = adjacent / hypotenuse

cos( 82 ) = 43.1 / x

x = 43.1 / cos( 82 )

x = 309.7 m

Therefore, the measure of x is 309.7 meters.

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Answer:

Option (A)

Step-by-step explanation:

By the characteristics of a quadrilateral given in the question,

1). All four sides are congruent.

It may be Square, Rhombus

2). Both the pairs of opposite sides are parallel.

It may be Parallelogram, Rhombus.

3). Diagonals are perpendicular.

It may be Rhombus, Rectangle, Square.

Since all three characteristics define the properties of a Rhombus,

The given quadrilateral matches with a rhombus.

Therefore, Option (A) will be the answer.

Answer:

26

Step-by-step explanation:

10 + 15

Answer:

Step-by-step explanation:

yes you would. they are very strict with food stamps or EBT card they will still ask for the 3 months for  so put in your 3 months and you should be fine.

The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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Answer:

C. It is just right

Step-by-step explanation:

Kermit's Favorite iced tea:

Tea bags = 15

Water = 2 liters

Ratio of tea bags to water = 15 : 2

= 15/2

= 7.5

Peggy:

Tea bags = 90

Water = 12 liters

Ratio of tea bags to water = 90 : 12

= 90/12

= 7.5

C. It is just right

Kermit would think of Peggy's iced tea is just right

Answer:

c

Step-by-step explanation:

Answer:

2(5(11) + 5(2.5) + 11(2.5))

= 2(55 + 12.5 + 27.5) = 2(55 + 40) = 2(95)

= 190 square centimeters

The range of the data is the difference between the highest and lowest values, which is 8 inches. Adding another plant with a height of 14 inches would not change the range, so the range would remain 8 inches.

Data is a collection of facts, figures, or information that can be processed and used to draw conclusions or make decisions. It can be stored in a variety of formats, including numerical, text, images, audio, and video. Data can be collected from a variety of sources, such as surveys, observations, experiments, or transactions. It can be used to inform decisions in areas such as business, health care, education, and research. Data can be analyzed to gain insight, develop strategies, identify trends, and make predictions. Data is a valuable resource and is increasingly important in today's digital age.

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The original price of the gourmet candy is $44, as per linear equation.

"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. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, 'x' is a variable, 'A' is a coefficient and 'B' is constant."

Given, the percent of discount at Dave's candy store is 15% = 0.15.

Sale price of a gourmet candy is $37.40.

Let, the original price of the gourmet candy is x.

Therefore, [x - (x × 0.15)] = 37.40

⇒ (x - 0.15x) = 37.40

⇒ 0.85x = 37.40

⇒ x = (37.40/0.85)

⇒ x = 44

Therefore, the original price of the gourmet candy is $44.

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The function is given to be:

The graph of the function is shown below:

The critical points are points where the function is defined and its derivative is zero or undefined.

The derivative is calculated to be:

The critical points are at f'(x) = 0:

Factoring:

Therefore, applying the zero factor principle:

or

Therefore, the critical numbers are given below with their descriptions:

Answer: The third one- x> four

Step-by-step explanation:

The circle is open, so it isn't equal to 4. That eliminates the top 2. The arrow is pointing to numbers greater than 4, so the answer is the third one.

Step-by-step explanation:

the area of a parallelogram is

baseline × height = 5 × 3.2 = 16 m²

Answer:

32 yards (squared)

Step-by-step explanation:

Length x width = area (LxW=A)

Step 1:

Length = 6 yards

Width = 5 1/3 yards

Step 2:

Multiply 6 x 5 1/3 because 6 is the length, 5 1/3 is the width, and LxW=A.

6 x 5 1/3 = 32 yards (squared)

The answer is :

− 2 8 − 2 5 − 7 2− 5

Answer:

im not sure on this but i think A. The linear parent function

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The V like shape comes from the function f(x)= lxl, which is the absolute value parent function

Answer:

A) 5² · 7

Explanation:

\(\sf 3^5\cdot 5^2\cdot 7^2\) = 3 · 3 · 3 · 3 · 3 · 5 · 5 · 7 · 7

and

\(\sf 5^3 \cdot 7\) = 5 · 5 · 5 · 7

Find common factors:

5 · 5 · 7

5² · 7

Answer:

As the sample size is large enough, i.e. n = 198 > 30 the central limit theorem can be applied to describe the sampling distribution for the sample proportion of children who are​ nearsighted.

Step-by-step explanation:

Let the random variable p denote the proportion of children affected by nearsightedness.

The previously known proportion was, p = 0.12.

A random sample of n = 198 children are selected.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

\(\mu_{\hat p}=p\)

The standard deviation of this sampling distribution of sample proportion is:

\(\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}\)

As the sample size is large enough, i.e. n = 198 > 30 the central limit theorem can be applied to describe the sampling distribution for the sample proportion of children who are​ nearsighted.

Answer:

y = 4

Step-by-step explanation:

distribute

10 + 2y = 18

minus 10 from both sides

2y = 8

divide by 2

y = 4

Answer: y=4

Step-by-step explanation:

2(5+y)=18

youre going to start by distributing the 2 to (5+y)

10+2y=18

then subract 10 from 18

2y=8

and then divide 2 on both sides

y=4