3(x − 2) = 12 nvwdksbvjkdsbvjkds jksncjv

\(15 + ( - 2) + - 9 = 13 - 9 = 4\)

#Goodluck!

Answer:

a) P(X<3)=0.964

P(X≤3)=0.995

b) P(X≥4)=0.005

P(1≤X≤3)=0.532

d) E(X)=0.75

Sigma=0.056

e) P(x=0)=0.077

Step-by-step explanation:

We have a binomial distribution with parameters n=15 and p=0.05.

The probabiltiy that k children, out of a sample of 15 children, have a food allergy can be calculated as:

\(P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{15}{k} 0.05^{k} 0.95^{15-k}\\\\\\\)

a) P(X<3) can be calculated as the sum written as:

\(P(x<3)=P(x=0)+P(x=1)+P(x=2)\\\\\\P(x=0) = \dbinom{15}{0} p^{0}(1-p)^{15}=1*1*0.463=0.463\\\\\\P(x=1) = \dbinom{15}{1} p^{1}(1-p)^{14}=15*0.05*0.488=0.366\\\\\\P(x=2) = \dbinom{15}{2} p^{2}(1-p)^{13}=105*0.0025*0.513=0.135\\\\\\\\P(x<3)=0.463+0.366+0.135=0.964\)

We can use this result to calculate P(X≤3) as:

\(P(x\leq3)=P(x<3)+P(x=3)\\\\\\P(x=3) = \dbinom{15}{3} p^{3}(1-p)^{12}=455*0.0001*0.54=0.031\\\\\\\\P(x\leq3)=0.964+0.031=0.995\)

b) We can calculate P(X≥4) as:

\(P(X\geq4)=1-P(X<4)=1-P(x\leq3)\\\\P(X\geq4)=1-0.995=0.005\)

We can calculate P(1≤X≤3) as:

\(P(1\leq x\leq3)=P(x=1)+P(x=2)+P(x=3)\\\\P(1\leq x\leq3)=0.366+0.135+0.031=0.532\)

c) The mean and standard deviation can be calcalated as:

\(E(x)=n\cdot p=15\cdot0.05=0.75\\\\\sigma=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.05\cdot0.95}{15}}=\sqrt{0.00317}=0.056\)

d) We can calculate this as the probability of a child not having an alergy, multiplied 50 times:

\(P(x=0)=(1-p)^{n}=0.95^{50}=0.077\)

The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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Answer:

a number that is at least as large as 8.9

Step-by-step explanation:

the line under the greater than sign makes it equal to or greater than

Answer:

Sonya got 16 questions correct.

Step-by-step explanation:

8/10=80%

80%×20=16

(To check)

16/20=80%

a. The mass of the apple is approximately 33.879 grams.

b. The volume of the apple increases by approximately 1.454 cubic inches during the five-week period.

a. To find the mass of the apple, we need to calculate its volume first. The circumference of the apple can be used to determine its radius.

The formula for the circumference of a circle is C = 2πr,

where C is the circumference and r is the radius.

Rearranging the formula, we have r = C / (2π).

Plugging in the given circumference of 6 inches.

we get r = 6 / (2π) ≈ 0.955 inches.

Now, we need to convert the radius from inches to centimeters since the density is given in grams per cubic centimeter.

Since 1 inch is approximately 2.54 centimeters, the radius in centimeters is \(0.955 \times 2.54\)  ≈ 2.427 cm.

Next, we can calculate the volume of the apple using the formula for the volume of a sphere: V = (4/3)πr³.

Plugging in the radius in centimeters, we get

V ≈ (4/3)π(2.427)³ ≈ 73.682 cm³.

Finally, we can find the mass of the apple by multiplying the volume by the density:

mass = volume \(\times\) density

= 73.682 cm³ \(\times\) 0.46 g/cm³

≈ 33.879 grams.

Therefore, the mass of the apple is approximately 33.879 grams.  

b. The volume of a sphere increases with the cube of its radius.

Since the radius increases by 1/8 inch per week for five weeks, the change in radius would be\((1/8) \times 5 = 5/8 inch.\)

Now, let's calculate the change in volume during the five-week period. The formula for the volume of a sphere is V = (4/3)πr³.

Initially, the radius was 0.955 inches.

After five weeks, the radius would be 0.955 + 5/8 inches.

To compare the change in volume, we can calculate the new volume and find the difference:

Change in Volume = New Volume - Initial Volume

Initial Volume = (4/3)π(0.955)³

New Volume = (4/3)π(0.955 + 5/8)³

By subtracting the initial volume from the new volume, we can determine how the volume changes during the five-week period.

Please note that the exact calculation will depend on the precise values used for π and the measurements provided.

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Answer:

j = 139.99 + 139.99 * 0.08625

Answer:

Step-by-step explanation:

The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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Answer:

The denominators of the fractions are 2 and 10.

The fractions with numerators of 1 that have sum of 3 / 5  is calculated below

The sum of the fractions are 3 / 5. Each of the fractions have a numerator of 1. Therefore, let the denominators be x and y

1 / x + 1 / y = 3 / 5

Therefore,

1 / x  + 1 / y = 3 / 5

y + x / xy = 3 / 5

cross multiply

5y + 5x = 3xy

Using hit and trial method,

5(2) + 5(10) = 3(10)(2)

10 + 50 = 60

60 = 60

The values are same.

Therefore, the denominators are 2 and 10.

Step-by-step explanation:

Answer:

0.6 sandwiches.

Step-by-step explanation:

3/5 = 0.6

0.6 sandwiches will each child get.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

Three children are sharing five sandwiches evenly.

each get is,

=3/5

= 0.6

Hence, 0.6 sandwiches will each child get.

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Answer:

a. x2 + 10x + 25 should be the correct one

The transformation represents a reflection over the y = × line.

A. (x, y) → (-x, y)

A reflection over the y-axis is a transformation that flips a point or shape across the vertical line y = 0.

This means that points on the right side of the y-axis will be reflected to the left side, and vice versa.

Let's examine each option to determine which one represents a reflection over the y-axis.

A. (x, y) → (-x, y):

This transformation reflects the point across the y-axis.

For example, if we have a point (3, 2), after applying this transformation, it becomes (-3, 2).

This represents a reflection over the y-axis.

B. (x, y) → (-x, -y):

This transformation not only reflects the point across the y-axis but also flips it vertically.

For example, if we have a point (3, 2), after applying this transformation, it becomes (-3, -2).

This represents a reflection over the y-axis.

C. (x, y) → (y, x):

This transformation swaps the x and y coordinates of a point, which does not represent a reflection over the y-axis.

Instead, it represents a 90-degree rotation of the point.

D. (x, y) → (y, -x):

This transformation swaps the x and y coordinates of a point and negates the new x-coordinate.

It does not represent a reflection over the y-axis.

Instead, it represents a 90-degree rotation of the point in the counterclockwise direction.

Based on the explanations above, both options A and B represent a reflection over the y-axis.

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Answer:

\(x = 2.5\)

Step-by-step explanation:

Given

The attached figure

Required

Find x

To solve for x, we make use of the following equivalent ratio

\(x :3.5 = 5 : 7\)

Express as fractions

\(\frac{x}{3.5} = \frac{5}{7}\)

Make x the subject

\(x= \frac{5}{7}*3.5\)

\(x= \frac{5}{2}*1\\\)

\(x = 2.5\)

Let's begin by listing out the information given to us:

distance between Vincent & Frank = 32km

distance equivalent is given by 1km=0.62 miles​

We will convert the distance from km to miles using the conversion factor:

Find the point R that breaks the directed segmentre in a ratio of 1:3. given point P(-4,5) and point Q(4,1).​

we have that

PR/RQ=1/3

or

PR/PQ=1/(1+3) ------> PR/PQ=1/4

step 1

Find the horizontal distance between P and Q (PQx)

PQx=4-(-4)=8 units

we hve

PRx/PQx=1/4

solve for PRx (horizontal distance between P and R)

PRx=PQx/4 -------> PRx=8/4=2

Find the x-coordinate of point R (Rx)

Rx=Px+PRx -----> Rx=-4+2=-2

the horizontal coordinate of R is -2

step 2

Find the vertical distance between P and Q (PQy)

PQy=5-1=4 units

we have

PRy/PQy=1/4

solve for PRy (vertical distance between P and R)

PRy=PQy/4 -----> PRy=4/4=1

Find the y-coordinate of point R (Ry)

Ry=Py-PRy ------> Ry=5-1=4

the y-coordinate of R is 4

therefore

Step-by-step explanation:

reflect the shape, will give you:

A = (-1,0)

B= (3, -5)

C= (-6, -7)

D= (-4, -1)

If a point A(x, y) is dilated by a factor P, the new point would be at

A'(Px, Py).

A = -1/2.5 = -0.4             0/2.5= 0

= ( - 0.4, 0)

B = 3/2.5 =  1.2              -5/2.5 = -2

= (1.2, -2)

C = -6/2.5= -2.4       -7/2.5 = -2.8

= ( -2,4, -2.8)

D = -4/2.5 = -1.6.     -1/2.5 = -0.4

= ( -1.6, -0.4)

You're Welcome!

Answer:

Step-by-step explanation:

( -1.6, -0.4)

If surface , S is the part of the sphere, x² + y²+ z² =1 ,lies above the cone, x² + y² = z

a)| ⃗rᵩ × ⃗rθ| = ⟨sin²φ cosθ,sin²φsinθ, sinφcosφ⟩

b)∫∫ z² ds = ₀∫ˣ₀∫ʸcos²φ dφdθ,

S

where x = 2π and y = π/4

A surface in space given in Cartesian coordinates as f(x,y,z) = 0, can be parametrized as a vector function with two parameters,

r(u,v)= ⟨r₁(u,v) , r₂(u,v) , r₃(u,v)⟩ , (u,v)∈R²

We have, S is a part of Sphere , x² + y²+ z² =1 , lies above the cone, x² + y² = z and surface S parametrized by following vector equation ,

r(θ, φ) = ⟨sinφ cosθ , sinφsinθ,cosφ⟩ --(1)

⃗rᵩ = ∂r/∂φ =⟨cos φ cosθ,cos φ sinθ,-sin φ⟩

⃗rθ= ∂r/∂θ=⟨- sinφ sinθ , sinφ cosθ ,0⟩

| ⃗rᵩ × ⃗rθ| =| i j k |

|cosφcosθ cosφ sinθ -sinφ |

|- sinφsinθ sinφ cosθ 0 |

= i( 0 + sinφ cosθsinφ) -j(0- (- sinφsinθ)(-sinφ)) + k(sinφ cosθ cosφcosθ - (-sinφ sinθ ) cosφ sinθ)

= (sin²φcosθ )i + (sin²φsinθ)j + (sinφcosφ(sin²θ+cos²θ))k

= sin²φcosθ )i + (sin²φsinθ)j +(sinφcosφ)k

| ⃗rᵩ× ⃗rθ|=⟨sin²φcosθ ,sin²φsinθ,sinφcosφ⟩

b) from part (a) we get,

x = sinφ cosθ

y = sinφsinθ

z = cosφ

are spherical coordinates of S where, 0≤φ≤π/4 and 0≤ θ≤ 2π.

so, ∫∫ z² ds = ₀∫ˣ₀∫ʸcos²φ dφ dθ ,

S

where x = 2π and y = π/4

So,Surface integeral is equals to ₀∫ˣ₀∫ʸcos²φ dφ dθ.

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Complete question:

If Sis the part of the sphere x2 + y2 + x2 = 1 that lies above the cone z= x2 + y2, find the following: a)S can be parametrized by a vector equation

r(θ, φ) = ⟨sinφ cosθ , sinφsinθ , cosφ ⟩ then a)| ⃗rᵩ × ⃗rθ| = ?

b) ∫∫ z² ds = ?

S

Hey there!

The answer is √20 or approximately 4.47

We can use the Pythagoreon Theorem, which is \(a^2 +b^2=c^2\). \(a\) and \(b\) are the names of the two sides, and \(c\) is the name of the hypotenuse leg, or the longest side. We will plug the numbers into the formula, and solve:

\(2^2+4^2=c^2\\4+16=c^2\\20=c^2\\4.47...=c\)

Have a terrifcly amazing day!

Answer:

87

Step-by-step

length x width=area

12*8=96-9=87

Answer:

  f(x) = (x +6)(x -5)  or  f(x) = x² +x -30

Step-by-step explanation:

You want a quadratic function whose zeros are -6 and +5.

If p is a zero of the polynomial f(x), then (x-p) is a factor. The two given zeros meant that the factors are ...

  f(x) = (x -(-6))·(x -5)

  f(x) = (x +6)(x -5) . . . . . . . . simplify a bit

This can be put in standard form by multiplying the factors:

  f(x) = x(x -5) +6(x -5) = x² -5x +6x -30

  f(x) = x² +x -30 . . . . . . . . simplified quadratic function

The quadratic function of the zeros is f(x) = \(x^2+x-30\).

What is quadratic function?

A polynomial function that has one or more variables and a variable having a maximum exponent of two is said to be quadratic. A polynomial of degree 2 is referred to as such because the greatest degree term in a quadratic function is of second degree. There must be at least one second-degree term in a quadratic function. It is a mathematical function.

Here the zeros of the function is -6 and 5.

We know that if zeros of the function is a then the factor is (x-a).

Then,

=> f(x) = (x-(-6))(x-5)

=> f(x) = (x+6)(x-5)

=> f(x) = \(x^2+6x-5x-30\)

=> f(x) = \(x^2+x-30\)

Hence the quadradic function is f(x) = \(x^2+x-30\).

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Using relations in a right triangle, the secant of angle θ is given by:

D. 5/4.

The relations in a right triangle are given as follows:

Using the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:

h² = 9² + 12²

h = sqrt(9² + 12²)

h = 15.

The secant of an angle is 1 divided by the cosine, hence:

Which means that option D is correct.

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Answer:

5. b = 3 m = 2

6. b = 5 m = 1/2

Step-by-step explanation:

5. Y-Intercept = 3

Slope = (13-3)/(5-0) = 10/5 = 2

6. Y-intercept 5

Slope = (6-5) / (2-0) = 1/2

Answer:

Angle JKN and Angle JKI are supplementary angles.

Step-by-step explanation:

When these two angles are added together, they will equal to 180 degrees.

Answer:

left bottom option

Step-by-step explanation:

when the value of their angles are added they sum up to be 180

The right angle triangle representing this scenario is shown below

A represents the beacon light

AB is the ship'e horizontal distance from the lighthouse

Taking angle A which is the angle of elevation as the reference angle,

opposite side = BC = 132

adjacent side = AB

To find AB, we would apply the tangent trigonomeric ratio which is expressed as

Tan # = opposite side/adjacent side

Therefore,

Tan 5 = 132/AB

ABtan5 = 132

AB = 132/tan5

AB = 1508.8

The ship's horizontal distance from the lighthouse and the shore is 1508.8 feet

Answer:

Maximum = 19

Minimum = 4

Median = 12

Step-by-step explanation:

The maximum number of phone sold per day is the value to the right of the horizontal axis as the values are arranged in ascending order ; Hence, the maximum number of phones sold per day is 19

Also, the minimum number of phones sold per day is the value to the left of the plot, Hence, minimum number of phones sold per day is 14.

The Median value : 4, 9, 14, 19

The median = 1/2(n+1)th term

1/2(5)th term = 2.5 th term

Median (9 + 14) /2 = 13 /2 = 11.5 = 12 phones

Answer:

-70, -18.5, -18 (least to greatest)

-70 < -18.5 (inequality statements)

-18.5 < -18

Step-by-step explanation:

Is this what you mean?

The instantaneous rate of change of y = √x at x = 2 is √2 / 2.

To find the instantaneous rate of change of y = √x at x = 2, we need to calculate the derivative of the function with respect to x and evaluate it at x = 2.

Taking the derivative of y = √x using the power rule for differentiation, we have:

dy/dx = (1/2) × x^(-1/2)

Now, substituting x = 2 into the derivative expression:

dy/dx = (1/2) × 2^(-1/2)

= (1/2) × √2

= √2 / 2

Therefore, the instantaneous rate of change of y = √x at x = 2 is √2 / 2.

None of the provided options (-1/2, -1/4, -1) are the correct instantaneous rate of change at x = 2.

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The minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

We are given that a water pumping station is to be built on a river at point P in order to deliver water to points A and B. The design requires that LAPD = /BPC so that the total length of piping that will be needed is a minimum. We need to find this minimum length of pipe.

The given figure is shown below: \(AB = 10 \ miles\)\(BC = 6 \ miles\)\(CP = 12 \ miles\). We are given that \(LAPD = LCPB\).

Now, we need to find the minimum length of pipe required for delivering the water to points A and B.The total length of the pipe, \(L_{total} = LA + AB + BP\)Since \(LAPD = LCPB\), we can say that\(AP^2 + PD^2 = BP^2 + PC^2\).

From the triangle ACP, we can say that\(AC^2 = AP^2 + PC^2\). So, we can substitute AP^2 + PC^2 with AC^2 to get\(AP^2 + PD^2 = BP^2 + AC^2\)Now, we can substitute AP = AC - PC and BP = BC + PC in the above equation to get\((AC - PC)^2 + PD^2 = (BC + PC)^2 + AC^2\).

After solving this equation, we get\(AC = \frac {37}{8}\) and \(PC = \frac {27}{8}\)Now, we can calculate the length of pipe required as follows: \(L_{total} = LA + AB + BP = 10 + 6 + \frac {27}{8} = \boxed{20.375 \ miles}\). Therefore, the minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

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