The Quotient of a number b and four plus seven is two

The chance density characteristic of lifetime in months of a transistor in a positive utility is:

[tex]f(x)=0.4cdot e^x > 0f(x)=0.4⋅e −0.4x ;x>0[/tex]

The chance density characteristic shows that the random variable X follows a exponential characteristic with parameter λ = 0.4.

Compute the suggest lifetime as follows:

[tex]mu=frac=2.5μ= λ1 = 0.401 =2.5[/tex]

Thus, the suggest lifetime is months.

Compute the usual deviation of the lifetimes as follows:

[tex]sigma=2.5σ= λ 2 1 = 0.40 2 1 =2.5.[/tex]

Thus, the usual deviation of the lifetimes is 2.5 months.

Compute the sixtieth percentile of the lifetime as follows:

Thus, the sixtieth percentile of the lifetime is 2.3 months.

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From the given options, Option A and Option D will represent the proportionality relation between x and y.

Equivalence between two variables that are related to one another and preserve a particular amount is referred to as a proportional relationship.

It is a mathematical concept that describes how two variables are related when they do so in equivalency and is also known as the "Relation of Proportionality."

Let the variables x and y are proportional to each other

=> x ∝ y

=> x = ky

=> x/y = k  [ where k is proportionality constant ]  

Here we will use the formula x/y = k to check the given variables' proportionality

Now check given options given below

Option A

x  0    1/5    2/5    3/5

y  0   1/10  2/10     3/10  

For  x = 1/5 and y = 1/10

=>  [tex]\frac{x}{y} = \frac{1}{5} \times \frac{10}{1}[/tex]  = 2

For  x = 2/5 and  y= 2/10

=>  [tex]\frac{x}{y} = \frac{2}{5} \times \frac{10}{2}[/tex]  = 2

Therefore, Table A represents the proportionality relation

Option B:

x -   0     1/2   1/3   1/4

y -   0     1/3   1/4   1/5

For  x = 1/2 and y = 1/3

=>  [tex]\frac{x}{y} = \frac{1}{2} \times \frac{3}{1}[/tex]  = 3/2

For  x = 1/3 and y = 1/4

=>  [tex]\frac{x}{y} = \frac{1}{3} \times \frac{4}{1}[/tex]  =  4/3  

Therefore, Table B doesn't represent the proportionality relation

Option C:

x -  0    1    3     5  

y -  0    1    9    25

For  x = 1 and y = 1

=>  [tex]\frac{x}{y} = \frac{1}{1} = 1[/tex]    

For  x = 3 and 9

=>  [tex]\frac{x}{y} = \frac{9}{3} = 3[/tex]  

Therefore, Table C doesn't represent the proportionality relation

Option D:

x -   0    1      3      4

y -   0    5    15    20

For  x = 1 and y = 5

=>  [tex]\frac{x}{y} = \frac{1}{5} = 1/5[/tex]    

For  x = 3 and y = 15

=>  [tex]\frac{x}{y} = \frac{3}{15} = \frac{1}{5}[/tex]  

Therefore, Table D will represent the proportionality relation

Therefore,

From the given options, Option A and Option D will represent the proportionality relation between x and y.

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The equation of the line normal to the curve y = square root(3x² + 2x) at point (2,4) is given as follows:

y - 4 = -4/7(x - 2).

The equation of the line normal to a curve follows the point-slope definition of a linear function, given as follows:

y - y' = m(x - x').

The function in this problem is defined as follows:

y = square root(3x² + 2x).

Then the derivative of the function, applying the chain rule, is given as follows:

y' = (6x + 2)/(2 x square root(3x² + 2x))

y' = (3x + 1)/square root(3x² + 2x)

At x = 2, the numeric value of the derivative is of:

y' = 7/square root(16) = 7/4.

The slope of the normal line is calculated as follows:

m x 7/4 = -1

m = -4/7.

(as the normal line is perpendicular to the tangent line, which has slope equals to the numeric value of the derivative at the point).

The coordinates of the point at (2,4), hence:

x' = 2, y' = 4.

Then the definition of the normal line is given as follows:

y - 4 = -4/7(x - 2).

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The graph of the function over the interval -2 ≤ x ≤ 2 is given below:

What do you mean by step function?

A piecewise function is one that is broken up into smaller functions, each of which has its own equation. A very particular (and much simpler) type of piecewise function is called a step function (or staircase function), and it has parts that resemble steps or the stairs of a staircase.

The graph of the function over the interval -2 ≤ x ≤ 2 is given below:

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A new form of the triple integral [tex]\int\limits^1_0 \int\limits^x_0 \int\limits^y_0 f(x,y,z)dzdydx[/tex] as a = 0 b = 1 g2(z) = 1 h2(y,z) = 1.

In other words, we want the integration order to be totally reversed for

[tex]\int\limits^1_0\int\limits^x_0 \int\limits^y_0 f (x,y,z) dz dy dx[/tex]

Keep in mind that this area is quite simple to define. The planes z = y and y = x, as well as the coordinate planes [tex]x=y=z=0[/tex], define our boundaries. We essentially have upper bounds z = y = x = 1 because x ∈[ 0, 1 ]. Therefore, we can alternatively express the region as:-

[tex]0\leq x\leq y\\0\leq y\leq z\\[/tex]

z∈ I0,1I. So

[tex]\int\limits^1_0 \int\limits^x_0 \int\limits^y_0 f(x,y,z)dzdydx = \int\limits^1_0 \int\limits^z_0 \int\limits^y_0 f(x,y,z)dxdydz[/tex]

Remember that a double integral could be set up in two different ways. Our number of alternative orders of integration increases from two to six when we include that third integral. We will rewrite the supplied integral in one of the other five possible orders in this exercise.

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The true or false values of the statements are:

From the question, we have the graph which represents the given parameters that can be used in our computation

Analysing the graph, we have:

The graph crosses the y-axis at y = 18

This means that the y-intercept of the graph is

y-intercept  = 18

This in other words mean that:

The cost of the book is $18

So, (a) is true

Also, the graph crosses the x-axis at x = 90

This means that the x-intercept of the graph is

x-intercept  = 90

This in other word mean that:

Giselle gets $18 if she pulls all the weed (i.e. 90 weeds) in the garden

So, (b) and (d) are true

The amount paid by her grandma is calculated as

Amount = 18/90

Amount = 1/5

So, (c) is true

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Considering definition of probability, the probability that a student chosen from the class at random has either blonde hair or brown hair is 36.

Probability is the possibility that a phenomenon or an event will happen, given certain circumstances and it is expressed as a percentage.

The union of events is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs and it is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

Two events, A and B, are incompatible when they have no element in common and it is true that P(A∩B)=0. Then:

P(A∪B)= P(A) + P(B)

You know:

The probability that a student chosen from the class at random has either blonde hair or brown hair is calculated as:

P(blond hair or brown hair)= P(blond hair) + P(brown hair)

Then:

P(blond hair or brown hair)= 12 + 24

P(blond hair or brown hair)= 36

Finally, the probability in this case is 36.

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The quadratic function in vertex form is formed as: f(x)=a(x + 2)² + 2.

        f(x)=a(x - h)² + k

For the stated question-

Whether you're going to increase by 2, you must also add 2.

The horizontal movement is determined by the h. It goes left or right depending on what you enter in h.

Finding the value that will cause the parenthesis to equal 0 when x equals -2 is necessary to make the necessary adjustments because shifting the vertex point to a left implies subtraction and negatives

x - h = 0

-2 - h = 0

-h = 2

h = -2

As a result, the function appears as follows:

f(x)=a(x - (-2))² + 2

A negative is subtracted to eliminate the signs and create a positive:

f(x)=a(x + 2)² + 2

Thus, the quadratic function in vertex form is formed as: f(x)=a(x + 2)² + 2.

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The total distance traveled by the object after 30.0 seconds is 450 meters.

For the stated function;

As, the total distance is modelled by the quadratic equation-

Let the quadratic equation be-

d = at² + bt + c

For (10, 50)

d = a(10)² + (10)b + c  ....eq 1

For (20, 200)

d = a(20)² + (200)b + c  ....eq 2

For (0, 0)

d = a(0)² + (0)b + c  ....eq 3

Solving eq 1, 2 and 3

a = 1/2 ; b = 0 and c =0

Thus, equation for the distance travelled by the object is-

d = 1/2 t²

For t = 30. sec

d = 1/2 (30)²

d = 450 m

Thus, the total distance traveled by the object after 30.0 seconds is 450 meters.

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The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).

We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;

x⁴ divided by 3x equals 2x³

3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³

subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27

3x³ divided by 3x equals x²

3x + 4 multiplied by x² equals 3x³ + 4x²

subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27

9x² divided by 3x equals 3x

3x + 4 multiplied by 3x equals 9x² + 12x

subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27

-15x divided by 3x equals -5

3x + 4 multiplied by -5 equals -15x - 20

subtract -15x - 20 from -15x + 27 will result to a remainder of 47

using the remainder theorem, x = -4/3 from the the divisor 3x + 4

thus:

f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}

f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27

f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}

f(-4/3) = (5919 - 2112)/81

f(-4/3) = 3807/81

f(-4/3) = 47

Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.

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Answer:

Answer Option C: SSA test

The lateral surface area of a prism having a base of 18 inches, 12 inches, and a height of 8 inches is 240 inches² and the total surface area is 672 inches².

The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas in addition to the lateral surface area.

Given:

The side of the base of the prism, A = 18 inches,

The side of the base of the prism, B = 12 inches,

The height of the prism, h = 8 inches,

Calculate the lateral surface area of the prism by the formula given below,

[tex]lateral \ surface \ area = Sum \ of \ sides\times height[/tex]

Lateral surface area = (A + B) × h

Lateral surface area = (18 + 12) × 8

Lateral surface area = 240 inches²

Now calculate the total surface area by the formula given below,

[tex]S = (2 \times Base \ Area) + (Base \ perimeter \times height)[/tex]

S = (2 × 18  × 12) + (18 + 12)  × 8

S = 432 + 240

S = 672 inches²

Therefore, the lateral surface area of a prism having a base of 18 inches, 12 inches, and a height of 8 inches is 240 inches² and the total surface area is 672 inches².

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The 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).

In the given question, the quality-control manager of a chemical company randomly sampled twenty 100-pound bags of fertilizer to estimate the variance in the pounds of impurities.

The sample variance was found to be 6.62.

We have to find a 95% confidence interval for the population variance in the pounds of impurities.

From the question,

N=20,

s^2=6.62

So, the Standard Deviation(SD) = √s^2

SD = √6.62

SD = 2.573

The confidence interval for the population variance is given by the following formula:

[tex]\frac{(n-1)s^2}{ \chi_{\alpha/2}} \leq\sigma^2\leq \frac{(n-1)s^2}{ \chi_{1-\alpha/2}}[/tex]

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculating the critical values. First we need to calculate the degrees of freedom given by:

df = n-1

df = 20-1

df = 19

Since the Confidence is 0.95 or 95%, the value of α=0.05 and α/2=0.025, and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.025,19)" "=CHISQ.INV(0.975,19)".

So for this case the critical values are:

[tex]\chi_{\alpha/2}[/tex] = 32.852

[tex]\chi_{1-\alpha/2}[/tex] = 8.907

Now putting the value in the formula:

[tex]\frac{19\times6.62}{32.852}\leq\sigma^2\leq\frac{19\times6.62}{8.907}[/tex]

3.829≤σ^2≤14.121

So the 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).

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Answer:

Step-by-step explanation:

the second because it has the squared sign most quadratic equations have squarred symbols

The probability of getting 5 face cards when taken without replacement is 0.00030473728.

There are 12 face cards in the deck overall.

When six cards are dealt, 12C5 equals 792.

without a replacement

P (5 face cards) = 12/5

P(5)=792 / 2598960 for five face cards.

P(5)=0.00030473728 for five face cards.

When 6 cards are picked from a deck without replacement, the likelihood of getting 6 face cards (a king, queen, or jack) is therefore 0.00030473728.

Probability is a branch of mathematics that deals with numerical descriptions of the likelihood that an event will occur or that a claim is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 indicates the event's impossibility and 1 indicates its certainty.

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The 95% confidence interval that estimates proportion of 8th graders that are involved in an after school activity (0.745, 0.895) , the correct option is (a) .

In the question ,

it is given that ,

simple random sample of 100 8th graders is taken ,

that means ,

n = 100 ,

also given that , 82% of them are involved with some type of after school activity.

means ; p = 0.82 .

the level of significance (α) = 100 - 95 = 5% = 0.05 .

the critical value=  [tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.025}[/tex] = 1.959964   ......from the Z table .

the lower limit of the 99% confidence interval is = p - [tex]Z_{\alpha /2}[/tex]*SE

and the upper limit for the 99% confidence interval is=  p + [tex]Z_{\alpha /2}[/tex]*SE  .

the standard error is √(p(1-p)/n

= √(0.82(1 - 0.82)/100

= 0.0384

So , the lower limit is ⇒ 0.82 - 1.959964*0.0384

On simplification ,

we get ,

lower limit is = 0.7447006 ≈ 0.745 .

the upper limit is =  p + [tex]Z_{\alpha /2}[/tex]*SE  

= 0.82 + 1.959964*0.0384

On Simplification ,

we get ,

upper limit is = 0.8952994 ≈ 0.895 .

Therefore , the confidence interval is (0.745, 0.895) .

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The area of the given irregular figure is 143 square inches.

What is area of irregular figure?

We divide an irregular shape into its component common shapes before calculating its area. After that, we add the areas of each shape. For instance, if a square and a triangle make up an irregular polygon, the area of the polygon is equal to the sum of their areas.

We have to divide the given irregular figure into known shapes.

That is rectangle and square.

Rectangles with sides '7 in and 10 in' and '12 in and 4 in' and the square of side 5 in.

So, the area of irregular figure is,

Area = Area of rectangle + Area of rectangle + Area of square

= (7 x 10) + (12 x 4) + 5^2

= 70 + 48 + 25

Area = 143

Hence, the area of the given irregular figure is 143 square inches.

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Answer:

is will end up costing 9.28

Step-by-step explanation:

all u need to do was divide the 4.06 by the 7 then the answer to that u multiple it by 16 and then u have ur final answer

Answer: $9.28

Step-by-step explanation:

Each bottle should cost 0.58 cents because 0.58 * 7=$4.06. SO if you multiply 0.58 by 16 (bottles) it will give you $9.28

The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The curve of the ball's path is given below.

d = -16t² + 32t + 9

The number of seconds to reach Jane is given as,

0 = -16t² + 32t + 9

16t² - 32t - 9 = 0

16t² - 36t + 4t - 9 = 0

4t(4t - 9) + 1(4t - 9) = 0

(4t - 9)(4t + 1) = 0

t = 9/4, -1/4

t = 2.25, -0.25

The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.

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1) The probability of F2 seed chosen at random will be yellow is the same as asking about the probability of forming a yellow seed in that generation. The answer is 3/4 (75%) because 1/4 = 25% GG is homozygous dominant and the rest 2/4 = 50% Gg are heterozygous.

2) In the F2 generation there are two genotypes that will breed true, which is homozygotic genotypes: GG and gg. But of these two, only one of them is yellow. The answer is 1/3 because from all the yellow seeds that resulted (GG, Gg and gG) only one has the genotype for true breeding.

3) The probability of taking out three seeds in which a least one is yellow can be calculated by subtracting the only  probability that doesn't fit the criterion, which is taking out a green seed 3 times:   = 1/64.

Then subtract that to 1  =  63/64

4) there are three possible groupings in which the green is taken once and the yellow seeds taken twice. The first possibility (follow the example) is the green being the first to come out, another possibility is being the second and the last possibility is being taken in the third time.

For example, Green yellow yellow- probability :

= 9/64

This is one possibily, but since there are 3, multiply it by 3 and you obtain the final answer:27/64.

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Answer:

box plot becauase wire width is numerical :)

Step-by-step explanation:

Answer:

its about the degrees.

Step-by-step explanation:

In a right triangle, the sum of the interior angles will always be 180°. Since a right angle is half that (90°), it has to be the biggest angle in the triangle and the side across from it will always be the longest.

To write 31/25 as a decimal, we can divide 31 by 25 using long division or a calculator and we get 1.24

A decimal is a way of expressing a number as a fraction of one.

Rounding off is a mathematical process that involves replacing a number with an approximate value that is easier to work with. When you round off a number, you choose the nearest whole number, ten, hundred, etc., depending on the place value you are rounding to.

For example, if you are asked to round the number 3.6 to the nearest whole number, you would round it off to 4, because 4 is the nearest whole number to 3.6.

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Answer:

50 degrees

Step-by-step explanation:

100 - 60 degrees

therorem

The ratio of p : q in its simplest form is 5 : 1

The unknown numbers are p and q

(p - 5) / (q - 5) = 9/1

(p + 20) / (q + 20) = 7/3

From equation (1)

cross product

1(p - 5) = 9(q - 5)

p - 5 = 9q - 45

p = 9q - 45 + 5

p = 9q - 40

From equation (2)

3(p + 20) = 7(q + 20)

3p + 60 = 7q + 140

Substitute p = 9q - 40 into 3p + 60 = 7q + 140

3p + 60 = 7q + 140

3(9q - 40) + 60 = 7q + 140

27q - 120 + 60 = 7q + 140

27q - 60 = 7q + 140

27q - 7q = 140 + 60

20q = 200

divide both sides by 20

q = 200/20

q = 10

Substitute q = 10 into p = 9q - 40

p = 9q - 40

p = 9(10) - 40

p = 90 - 40

p = 50

In conclusion, the ratio of p to q = 50 : 10

= 50/10

= 5/1

= 5:1

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For the given algebaric expression, 1.4f+1.1=8.3−f where "f " is variable the solved value of "f" is 3..

We have an algebraic expression of one variable say f ,

1.4 f + 1.1 = 8.3 - f --(1)

we have to solve it

Step 1 : Multiply both sides by 10

1.4 f ×10 + 1.1 ×10 = 8.3×10 - f ×10

=> 14/10(10f) + 11/10(10) = 83/10(10) - 10f

=> 14f + 11 = 83 - 10f

Step 2 : Subtract 11 from both sides

=> 14f + 11 - 11 = 83 - 10f -11

=> 14f = 72 - 10f

Step 3 : Add 10f both sides

=> 14f + 10f = 72 - 10f + 10f

=> 24f = 72

Step 4 : Divide both sides by 24

=> 24f/24 = 72/24

=> f = 3

Hemce,the solved value of "f" is 3 ..

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Initial velocity of the function = 109 ft/sec.

The given quadratic function is-

h(t) = -16t² + 109t

maximum height;

dh/dt = 0 and d²h/dt² < 0.

Then,

dh/dt = -32t + 109

dh/dt = 0

-32t + 109 = 0

t = 3.4 seconds.

Time when maximum height is reached by the ball is 3.4 second.

Maximum height;

h(t) = -16(3.4)² + 109(3.4)

h(t) = 185.6 ft

Thus, the maximum height obtained by the ball is 185.6 ft.

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The complete question is-

A ball is thrown vertically upward from the ground with an initial velocity of 109 ft/sec. Use the quadratic function

h(t) = -16t2 + 109t to find how long it will take for the ball to reach its maximum height, and then find the maximum height.