PLEASE I NEED HELP!! URGENT!!!

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Answer jake is 29

Step-by-step explanation:

Answer:

Step-by-step explanation:

let the age of Jake be=x

let the age of Finn be=x+4

Five years ago:

age of Jake +age of Finn=48

x+x+4-5=48

2x-1=48

2x=48=1

2x=49

x=49/2

x=24.5

therefore, age of Jake=x=24.5

therefore, age of Finn=x+4=24.5+4=28.5

hope it helps

Answer:

Rs. 4000

Step-by-step explanation:

Profit = 80% = 180% of original price

Therefore, \(\frac{180}{100}x=7200\\ 180x=720000\\x=4000\)

Answer:

9000

Step-by-step explanation:

80 percent *9000 =

(80:100)*9000 =

(80*9000):100 =

720000:100 = 7200

Using the proportional rule of Similar Triangles, the length of SD is 12 m.

Given a truss bridge.

From it,

The triangles BCD and RSD are similar.

For similar triangles, corresponding sides are proportional.

Corresponding sides are,

BC and RS, CD and SD, BD and RD.

BC / RS = CD / SD = BD / RD.

Consider BC / RS = CD / SD.

2 / 1 = 24 / SD

2 (SD) = 24

SD = 12

Hence the length of SD is 12 m.

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In this case, we are given only a partial list of observations. To determine if the process is in control, we would need the complete set of observations to evaluate their values in relation to the control limits.

To construct a control chart and determine if the process is in control, we need to calculate the control limits using the given observations.

Let's start by calculating the average (x(bar)) and standard deviation (σ) of the observations:

Observations: 10, 3, 9, 9, 8, 4

Step 1: Calculate the average (x(bar)):

x(bar) = (10 + 3 + 9 + 9 + 8 + 4) / 6 = 43 / 6 ≈ 7.17

Step 2: Calculate the standard deviation (σ):

1. Calculate the squared deviation for each observation:

\((10 - 7.17)^2, (3 - 7.17)^2, (9 - 7.17)^2, (9 - 7.17)^2, (8 - 7.17)^2, (4 - 7.17)^2\)

= 6.9129, 18.9129, 2.5929, 2.5929, 0.6889, 10.5889

2. Calculate the average of the squared deviations:

(6.9129 + 18.9129 + 2.5929 + 2.5929 + 0.6889 + 10.5889) / 6 ≈ 7.9198

3. Calculate the square root of the average squared deviation:

σ = √(7.9198)

≈ 2.81

Now that we have the average (x(bar)) and standard deviation (σ), we can construct the control chart using two sigma limits. The control limits are calculated as follows:

Upper Control Limit (UCL) = x(bar) + (2 * σ)

Lower Control Limit (LCL) = x(bar) - (2 * σ)

UCL = 7.17 + (2 * 2.81)

≈ 12.79

LCL = 7.17 - (2 * 2.81)

≈ 1.55

Based on the control chart, if any of the observations fall above the UCL or below the LCL, it would indicate an out-of-control process.

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Answer:

13

Step-by-step explanation:

In order to find u, we have to get u by itself. So first step is to divide both sides by 7, which you end up with:

\(u=\frac{91}{7}\)

and this simplifies to

u=13

Answer:

(x + 4)

Step-by-step explanation:

x - 2 = 0, so x = 2

x - 4 = 0, so x = 4

x - 6 = 0, so x = 6

The option which is not a factor of the cubic equation is (x+4)

The algebraic equations having variables with power 3 are referred to as cubic equations. A generalized form of a cubic equation is ax³+ bx²+ cx + d = 0.

Given here: The cubic function f(x)=x³-12x²+44x-48

Clearly in the options the list of factors are -4,6,2,4

Checking for all 4 options we get

f(-4)=-4³-12×4²+44×(-4)-48

     =-64-192-176-48≠0

f(6)=6³-12×6²+44×(6)-48

    =216-12×36+264-48

    =0

f(2)=2³-12×4+44×2-48

    =8-48+88-48

    =0

Similarly we can find for x=4 that f(4)=0

Hence, The option which is not a factor of the cubic equation is (x+4)

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Step-by-step explanation:

come on !

how do you create a line ?

you mark 2 points, take a ruler and draw a line through both points (and extend the line beyond the points as far as the chart goes).

how do you find points ?

you think about a nice value for x (really, any value on the x-axis of the chart is OK) and then calculate y.

you mark the point at this x, y coordinates.

you know, the x-axis is the horizontal coordinate line, and the y-axis is the vertical coordinate line.

so, I would pick x =0. that gives us y = 0 + 0.5 = 0.5.

and maybe x = 2. that gives us y = 2 + 0.5 = 2.5

so, you have (0, 0.5) and (2, 2.5) as points.

and then simply do as described above.

Answer:

The value of k is -3.

Explanation:

To determine the value of k, first, find the equations of f(x) and g(x) using the two-point form of the equation of a line.

The indicated points on f(x) are (0,1) and (1,-1).

Similarly, the indicated points on g(x) are (1,3) and (0,-3).

Therefore, we have that:

The value of k is -3.

Answer:

.12 km/min.

Step-by-step explanation:

1.8 kilometers / 15 minutes = .12 kilometers per minute

Answer:

40

Step-by-step explanation:

30÷3=10

30+10=40

Hope this helps! :)

Answer:

- 19

Step-by-step explanation:

- 19 has the least value

The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

ANSWER

$6000

EXPLANATION

We have that Bob invested $15,000 in the Fund A with 3% profit.

Let the amount he invested in Fund B with 10% profit be x.

Let the total amount invested in both accounts be y.

We need to find x.

This means that:

y = 15000 + x ____(1)

Both accounts returned 5% profit, so:

(15000 * 3) + (x * 10) = (y * 5)

=> 45000 + 10x = 5y ____(2)

Put (1) in (2):

45000 + 10x = 5(15000 + x)

45000 + 10x = 75000 + 5x

Collect like terms:

10x - 5x = 75000 - 45000

5x = 30000

x = 30000 / 5

x = $6000

Therefore, he invested $6000 into Fund B.

The consumption bundle that will not be the consumer's choice, given the assumptions of choosing the optimal bundle, is option B) 30 snacks and 12 meals. To determine the optimal consumption bundle, we need to consider the consumer's budget constraint and maximize their utility.

Given that the price of snacks is $4 and the price of meals is $10, and the consumer has $240 remaining on their meal card, we can calculate the maximum number of snacks and meals that can be purchased within the budget constraint.

For option A) 5 snacks and 20 meals, the total cost would be $4 × 5 + $10 × 20 = $200. Since the consumer has $240 remaining, this bundle is feasible.

For option B) 30 snacks and 12 meals, the total cost would be $4 × 30 + $10 × 12 = $240. This bundle is on budget constraint, but it may not be the optimal choice since the consumer could potentially consume more meals for the same cost.

For option C) 20 snacks and 16 meals, the total cost would be $4 × 20 + $10 × 16 = $240. This bundle is also on budget constraint.

Since options A, C, and D are all feasible within the budget constraint, the only bundle that will not be the consumer's choice is option B) 30 snacks and 12 meals. The consumer could achieve a higher level of utility by reallocating some snacks to meals while staying within the budget constraint. Therefore, the correct answer is option B.

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The equation of a circle with center (a, b) and radius r is:

(x - a)^2 + (y - b)^2 = r^2

(x, y) represents any point on the circle

A circle is described as a shape consisting of all points in a plane that are at a given distance from a given point, the center.

The properties of the circle are as follows:

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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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Answer:

Amm

19, B(16) it is 16 ......

The critical value tα/2 for a 99% confidence level with 36 degrees of freedom is 2.72. The margin of error is E = 2.72 * (0.00568 / sqrt(36)) = 0.00258 lb. The confidence interval estimate of μ is 0.82151 lb to 0.82667 lb at a 99% confidence level.

(a) The critical value tα/2 for a 99% confidence level with 36 degrees of freedom can be obtained from a t-table or a statistical software. For simplicity, let's assume the critical value is 2.72.

(b) The margin of error (E) can be calculated using the formula: E = tα/2 * (s / sqrt(n)), where tα/2 is the critical value, s is the sample standard deviation, and n is the sample size. Plugging in the given values, we have:

E = 2.72 * (0.00568 / sqrt(36)) = 0.00258 lb

(c) The confidence interval estimate of μ (the population mean) can be calculated by subtracting and adding the margin of error to the sample mean. In this case, the sample mean (x) is given as 0.82409 lb. Therefore, the confidence interval is:

0.82409 lb - 0.00258 lb ≤ μ ≤ 0.82409 lb + 0.00258 lb

0.82151 lb ≤ μ ≤ 0.82667 lb

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The complete factorization of 3x⁵- 75x³ is:- 3x³(x + 5)(x - 5)

How to solve factor?

To factor completely the expression 3x⁵ - 75x³, we can first factor out the greatest common factor (GCF) of the two terms, which is 3x³:

3x³(x² - 25)

Next, we can factor the expression inside the parentheses using the difference of squares formula:

3x³(x + 5)(x - 5)

Therefore, the complete factorization of 3x⁵ - 75x³ is:

3x³(x + 5)(x - 5)

We can check that this is the correct factorization by using the distributive property of multiplication and verifying that the product of the factors is equal to the original expression:

3x³(x + 5)(x - 5) = 3x³(x² - 25)

= 3x³x² - 3x³(25)

= 3x⁵ - 75x³

So the factorization is correct.

In summary, to factor completely an expression like 3x⁵ - 75x³, we should first factor out the GCF and then look for further factorization opportunities using various factorization techniques such as the difference of squares formula, the sum or difference of cubes formula, or the quadratic formula. It's important to remember to check our work by multiplying the factors back together to ensure that we get the original expression.

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Answer:

13 Student.

Step-by-step explanation:

Decreased = Subtract

35% = .35

20 x .35=7

20-7= 13

Hence, You have 13 student now.

[RevyBreeze]

Answer:

c. is the answer

The completed table of the slopes of the two triangles that have their longest side on the same line is presented as follows;

Triangle \({}\)  Vertical side     Horizontal side       \(\dfrac{Vertical}{Horizontal}\)

RST \({}\)             2                     4                             2/4 = 1/2

XYZ \({}\)             3                     6                             3/6 = 1/2

The slope of a line on the coordinate plane is the ratio of the rise to the run of the line.

a. The length of the vertical side of triangle ΔRST = 2 units

The length of the horizontal side of triangle ΔRST = 4 units

The slope of the longest side is \(Slope =\dfrac{Vertical}{Horizontal}\)

Therefore;

\(Slope = \dfrac{2}{4} = \dfrac{1}{2}\)

The slope of the longest side of triangle ΔRST is 1/2

The length of the vertical side of triangle ΔXYZ = 3 units

The length of the horizontal side of triangle ΔXYZ obtained by counting the unit squares = 6 units

The slope of the longest side of triangle ΔXYZ is therefore;

\(Slope =\dfrac{3}{6} = \dfrac{1}{2}\)

The slope of the longest side of triangle ΔXYZ is 1/2

b. Two triangles are similar if two angles in one triangle are congruent to two triangles of the other triangle.

The triangles ΔRST and ΔXYZ are right triangles, therefore, they each have a 90° angle

The slope of the longest side, RT, of triangle ΔRST is the same as the slope of the longest side, XZ, of triangle, ΔXYZ, therefore, the lines RT and XZ are segments of the same line and the angle they form with the horizontal, ∠TRS and ∠ZXY are congruent, therefore;

ΔRST is similar to ΔXYZ by the Angle-Angle, AA, similarity postulate

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

let number be x

1/6x - 1/12x= 4

1/12x=4

cross multiply

x= 12 x 4

x= 48

If one-sixth of a certain number is four more than one-twelfth the number, the required number will be 48.

Let the unknown number be 'a'

One-sixth of the number is expressed as 1/6 a ..... 1

One-twelfth the number is also expressed as 1/12 a

Four more than one-twelfth the number will be written as:

1/12 a + 4 .... 2

Equating 1 and 2 will give:

1/6 a = 1/12 a + 4

a/6 = a/12 + 4

Collect the like terms

\(\frac{a}{6} - \frac{a}{12} = 4\)

Find the LCM

\(\frac{2a-a}{12} = 4\\\frac{a}{12} = 4\)

Cross multiply

a = 12×4

a = 48

This shows that the required number is 48

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The congruency statement for the two triangles is:

∆FGH ≅ ∆JKL

To determine if triangles ∆FGH and ∆JKL are congruent, we need to compare the corresponding sides and angles of the two triangles.

Let's start by finding the lengths of the sides of each triangle:

∆FGH:

Side FG: Distance between F(-5, 10) and G(-2, 2)

= √[(-2 - (-5))^2 + (2 - 10)^2]

= √[3^2 + (-8)^2]

= √[9 + 64]

= √73

Side GH: Distance between G(-2, 2) and H(-9, -7)

= √[(-9 - (-2))^2 + (-7 - 2)^2]

= √[(-7)^2 + (-9)^2]

= √[49 + 81]

= √130

Side FH: Distance between F(-5, 10) and H(-9, -7)

= √[(-9 - (-5))^2 + (-7 - 10)^2]

= √[(-4)^2 + (-17)^2]

= √[16 + 289]

= √305

∆JKL:

Side JK: Distance between J(0, -5) and K(9, 2)

= √[(9 - 0)^2 + (2 - (-5))^2]

= √[9^2 + 7^2]

= √[81 + 49]

= √130

Side KL: Distance between K(9, 2) and L(-8, -2)

= √[(-8 - 9)^2 + (-2 - 2)^2]

= √[(-17)^2 + (-4)^2]

= √[289 + 16]

= √305

Side JL: Distance between J(0, -5) and L(-8, -2)

= √[(-8 - 0)^2 + (-2 - (-5))^2]

= √[(-8)^2 + 3^2]

= √[64 + 9]

= √73

By comparing the side lengths, we see that ∆FGH and ∆JKL have the same lengths for all three sides: FG ≈ JK ≈ √73, GH ≈ KL ≈ √130, and FH ≈ JL ≈ √305.

Since all corresponding sides have the same lengths, we can conclude that ∆FGH and ∆JKL are congruent.

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Answer:

To find the slant height of a pyramid, you need to know the length of the base and the height of the pyramid The slant height can be found using the Pythagorean theorem, which states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The formula for the slant height of a pyramid is:

Slant height = √ (Base² + Height²)

For example, if the base of a is 10 meters and the height is 20 meters, then the slant height is:

Slant height = √ (10² + 20²) = √500 = 10√5 meters

Answer: We can find slant height of pyramid by using pythagorean theorem which states that (height)^2 + (half lateral edge length)^2 = (slant height)^2.

Step-by-step explanation:

To find the slant height of pyramid we need to know the height of the pyramid and the lateral edge length.

The height of the pyramid is the perpendicular distance from the base to the apex. The lateral edges are the edges that connect apex to the vertices of the base.

Applying pythagorean theorem, we can calculate the slant height of the pyramid by using the formula-

(slant height)^2 =  (height)^2 + (half lateral edge length)^2

or simply we can write as:  \(s= \sqrt{h^{2} + (l/2)^{2}\).

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The measure of this angle in degrees is 20.52 degrees.

Step by step explanation:Given data is,1/360th of the circumference of the circle is 0.59 cm long Arc length, s = 103.25 cm We need to find the measure of the angle in degrees. Since we know that, the angle subtended by an arc at the center of the circle is 2θ, where θ is the angle subtended by the arc at any point on the circumference of the circle.And the circumference of the circle is 360θ.

Hence, we can find the length of the circumference of the circle. Circumference of the circle = 360 × 0.59Circumference of the circle = 212.4 cmNow, we can find the radius of the circle.r = s/2πr = 103.25/(2 × π) = 16.441 cmDiameter of the circle = 2 × rDiameter of the circle = 32.882 cmThe circumference of the circle = πdCircumference of the circle = π × 32.882Circumference of the circle = 103.26 cm Now, we can find the angle of the circle. Angle of the circle = 360θ103.26 = 360θθ = 103.26/360θ = 0.286 degrees So, the measure of this angle in degrees is 20.52 degrees.

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