Guys I need help with this question number 4 the topic is called Simultaneous equations

Answer:

The formula for the surface area of a cuboid is:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the cuboid, respectively.

In this case, l = 6 cm, w = 4 cm, and h = 3 cm. Substituting these values into the formula, we get:

SA = 2(6)(4) + 2(6)(3) + 2(4)(3)

SA = 48 + 36 + 24

SA = 108

Therefore, the surface area of the cuboid is 108 square centimeters.

Step-by-step explanation:

Answer: Surface Area is [tex]72cm^2[/tex].

Step-by-step explanation: Let surface area be a.

[tex]a= 2(5*4)+(5*2)+(4*2)\\a= 2(20+10+8)\\a=2(38)\\a=72 cm^2[/tex]

This means the surface area of the solid cuboid is [tex]72cm^2[/tex].

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The 8 students at the pizza party ate 2 and 2/3 pizzas if each student ate 1/3 of a pizza.

If each of the 8 students ate 1/3 of a pizza, we can find the total number of pizzas by multiplying the number of students by the fraction of a pizza each student ate:

8 students × 1/3 pizza per student = 8/3 pizzas

However, it's more common to express the result as a mixed number or decimal. To convert the improper fraction 8/3 to a mixed number, we can divide the numerator by the denominator:

8 ÷ 3 = 2 with a remainder of 2

Therefore, the students ate 2 and 2/3 pizzas altogether. Alternatively, we can convert the improper fraction to a decimal by dividing the numerator by the denominator:

8/3 = 2.67

Therefore, the students ate approximately 2.67 pizzas altogether.

To recap, if each of the 8 students at the pizza party ate 1/3 of a pizza, they ate 8/3 pizzas altogether, which is equal to 2 and 2/3 pizzas or approximately 2.67 pizzas.

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Based on the given task content; the decrease of R1400 in the ratio 7:3 is R980 and R420 respectively.

Ratio refers to the number representing a comparison between two different quantities. It is expressed as a quotient which is the relative magnitudes of two quantities.

Amount given = R1400

Ratio = 7 : 3

Total ratio = 7 + 3 = 10

Rate 1 for 7:

= 7/10 × R1400

= 0.7 × R1400

= R980

Rate 2 for 3:

= 3/10 × R1400

= 0.3 × R1400

= R420

In conclusion, R1400 decreased in the ratio 7:3 is R980 and R420.

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Answer:

To solve this expression, we can use the order of operations, which tells us to perform the operations inside the parentheses first, and then multiply by -2.

So, we have:

(12 + 13) (-2)

= (25) (-2) // simplify the parentheses by adding 12 and 13

= -50 // multiply 25 by -2

Therefore, (12+13)(-2) equals -50.

Answer:

If you multiply a function by a constant value, it will result in a vertical scaling of the graph. In this case, multiplying by 1/3 would compress the graph vertically by a factor of 3. Specifically, the y-coordinates of each point on the graph would be multiplied by 1/3, resulting in a graph that is one-third as tall as the original.

Step-by-step explanation:

4x^3 + 7x^2 + 10    <====standard form

    degree  is 3 (this is the largest exponent)     and there is three terms

Since Lourdes garage is in the shape of a square pyramid, the surface area of the square pyramid roof is 1440 ft²

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The surface area (SA) of a pyramid is given as:SA = B + (1/2)Ph

where B is the base area, P is the perimeter and h is the slant height

Since the roof is a square pyramid with base 40 feet and slant height of 18 ft, hence:

h = 18 ftP = 40 + 40 + 40 + 40 = 160 ft.

Surface area of only roof = (1/2)Ph

Therefore, Substituting:

SA = (1/2)(160)(18) = 1440 ft²

The surface area of the roof is 1440 ft²

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Answer: -2

Step-by-step explanation: Find the midpoint of both points so they are equidistant meaning that the ratios between them are 1:1.

To do so, add both quantities given and divide by 2.

[tex](-7+3)/2\\(-4)/2\\-2[/tex]

Which is the answer!

Answer:

plot the point at -2

Step-by-step explanation:

According to the problem, Alvin is 12 years younger than Elga, and the sum of their ages is 66. So, we have to use algebra to find Elga's age.

Step-by-step explanation:

Let's assume Elga's age to be x.

Alvin's age can be found as: x - 12

The sum of their ages is 66. So,

x + (x - 12) = 66 ⇒ 2x - 12 = 66

⇒ 2x = 78

⇒ x = 39

Therefore, Elga's age is 39 years old.

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A recursive formula for this geometric sequence is;

Option C:

a₁ = -1/8

aₙ = (-1/8)a⁽ⁿ⁻¹⁾

The geometric sequence is given as;

-1/8, -1/4, -1/2, -1, . . .

The general formula used to find the nth term of a geometric sequence is;

aₙ = a(r)⁽ⁿ⁻¹⁾

where;

a is first term

d is common ratio

where;

r = (-1/4)/(-1/8)

r = 2

Thus;

aₙ = -1/8(2)⁽ⁿ⁻¹⁾

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Answer: The answer would be about 38.88 meters

Step-by-step explanation:

First you transfer Kilometers per hour into Meters per second.

35 KM/H = 9.72 M/S

The formula for distance is D = Speed x Time

9.72 x 4 seconds = 38.88 Meters that he will travel in 4 seconds

630 .18 feet tall is the gateway arch by the trigonometric ratio

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.

As given

The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St. Louis, Missouri is 39 degrees.

Now by using the trigonometric property

[tex]tan\theta=\frac{P}{B}[/tex]

As the diagram is given below.

AB=CB tan39

AB = 778 tan 39

AB= 630.18 feet

Hence the gateway arch is 630.18 feet tall.

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Answer:

a) 20 minute=2pi/3 rad

angle=arc length/radius

arc length= angle×radius

               =2pi/3×2.5

               =5pi/3 cm

b)area= pi(radius)²/2

           =pi×6.25

           =25pi/4cm²

i hope you find it helpful

Step-by-step explanation:

Answer:

[tex]L=\frac{5}{3} \pi cm. \\ A=3.125\pi cm^{2}[/tex]

Step-by-step explanation:

a)

L - is how far does the tip of the hand move in diameter.

m - is how much time does the tip of the hand move in minutes.

m=20

r =2,5cm

[tex]L=\frac{m}{60} *2\pi r\\L=\frac{20}{60} *2\pi *2,5cm\\L=\frac{5}{3} \pi cm[/tex]

In a formula, we have  [tex]\frac{m}{60}[/tex]  because the minute hand needs 60 minutes to make one circle. L = 2πr is a formula for the full length of a circle.

b)

A- Area

r=2,5cm

m - is how much time does the tip of the hand move in minutes.

[tex]A=\frac{m}{60} *\pi r^{2} \\A=\frac{30}{60} *\pi *(2,5cm)^{2} \\A=\frac{1}{2} *\pi *6.25cm^{2} \\A=3.125\pi cm^{2}[/tex]

In the formula, we have  [tex]\frac{m}{60}[/tex]  because the minute hand needs 60 minutes to make one circle. The formula for the full area of a circle is A=πr².

The value of k that solves the proportion is given as follows:

k = 100/9.

The proportional relationship for this problem is defined as follows:

9/10 = 10/k.

Then we cross-multiply, that is we multiply the numerator of one ratio by the denominator of the other ratio, and vice versa, hence:

9k = 10 x 10

9k = 100.

Then we solve for the unknown variable k, applying the division, which is the inverse operation of the multiplication, hence the value of k that solves the proportion is given as follows:

k = 100/9.

The proportional equation for this problem is defined as follows:

9/10 = 10/k.

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Answer:

17

Step-by-step explanation:

To find the median of 16 even numbers, we need to arrange the numbers in order from least to greatest, and then find the middle value.

Since the numbers are even, the middle two values will need to be averaged to find the median.

Let's assume the 16 even numbers are:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32

Now, we arrange them in order from least to greatest:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32

The middle two numbers are 16 and 18. So, we need to average them to find the median:

Median = (16 + 18) / 2 = 17

Therefore, the median of 16 even numbers is 17.

Using the length and breadth οf the rectangular kitchen, fοund using the distance fοrmula, we fοund the area as 165 sq. feet.

The internal angles οf a rectangle, which has fοur sides, are all exactly 90 degrees. At each cοrner οr vertex, the twο sides cοme tοgether at a straight angle.

Here, Pοints (7,6) and (7.-9) lie οn the same hοrizοntal line as the x values are the same

Sο the distance between these pοints can be taken as the length οf the rectangle.

The distance can be fοund using the distance fοrmula.

Length l = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

             = [tex]\sqrt{(7-7)^2 + (6--9)^2} = \sqrt{15^2} = 15[/tex]

Nοw the pοints  (7,6) and (-4,6) lie οn the same vertical line as the y values are the same.

Sο the distance between these pοints can be taken as the breadth οf the rectangle.

Breadth b = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex] = [tex]\sqrt{(7--4)^2 + (6-6)^2} = \sqrt{11^2} = 11[/tex]

Since it is a rectangle, the οppοsite sides will have the same measurements.

Nοw the area = l * b = 15 * 11 = 165 sq. feet.

Therefοre using the length and breadth οf the rectangular kitchen, fοund using the distance fοrmula, we fοund the area as 165 sq. feet.

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27 mn is the length of line segment .

What in mathematics is a line segment?

A line segment has two unique points on the line defining its boundaries. Or, a line segment is a section of the line that links two points, as another alternative.

                            In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are fixed or identifiable.

The value of the line segment will be calculated as:-

Point M is on the line segment MN.

  In = 20

  Im = 7

 MN = In+ Im

       = 20 + 7

       = 27

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Mr. Yang invested the $1000 approximately 8.55 years ago

To calculate the time that Mr. Yang invested the money, you can use the formula for compound interest: A=P(1+r/n)^nt where A is the amount of money after t years, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years. We are given A= $1435.77, P=$1000, r=0.06, and n=2 (since interest is compounded twice per year). We want to solve for t, so we will rearrange the formula to solve for t:t=ln(A/P)/(n ln(1+r/n))Plugging in the values, we have: t= ln(1435.77/1000)/(2 ln(1+0.06/2)) ≈ 8.55 years, rounded to two decimal places.Therefore, Mr. Yang invested the $1000 approximately 8.55 years ago.

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Answer:

Step-by-step explanation:

To find the volume of a sphere, we use the formula:

V = (4/3) * π * r^3

where r is the radius of the sphere.

We are given that the radius of the sphere is 7 cm and we can use 3 as an approximation for π. Substituting these values in the formula, we get:

V = (4/3) * 3 * 7^3

V = (4/3) * 3 * 343

V = 4 * 343

V = 1372

Therefore, the volume of the sphere is 1372 cubic centimeters.

Answer:

[tex]\huge\boxed{\sf x = 6.5 }[/tex]

Step-by-step explanation:

Given that, both the expressions are equal.

So,

7x - 5 = 5x + 8

7x - 5x - 5 = 8

2x - 5 = 8

2x = 8 + 5

2x = 13

x = 13/2

[tex]\rule[225]{225}{2}[/tex]

Answer:

[tex] \sf \: x = 6.5[/tex]

Step-by-step explanation:

Given expressions,

→ 7x - 5

→ 5x + 8

Now we have to,

→ Find the required value of x.

Forming the equation,

→ 7x - 5 = 5x + 8

Then the value of x will be,

→ 7x - 5 = 5x + 8

→ 7x - 5x = 8 + 5

→ 2x = 13

→ x = 13 ÷ 2

→ [ x = 6.5 ]

Hence, the value of x is 6.5.

Answer:

y = 2/3x - 2

Step-by-step explanation:

Part A:  The amount of unearned interest is $3,225.

Part B: The amount needed to repay the loan using the Rule of 78 is $8,443.75.

Part C: To support our answers to Part A and Part B, the total interest that Christopher would have paid, which is 3,900$. the amount needed to repay the loan using the Rule of 78, which is $8,443.75.

What is an interest?

To determine the amount of unearned interest, we need to find out how much interest Christopher would have paid if he made all 24 payments.

First, we can calculate the total amount he would have paid if he made all 24 payments:

Total amount paid = 475 x 24 = 11,400$

Next, we can subtract the amount borrowed from the total amount paid to find the total interest:

Total interest = Total amount paid - Amount borrowed

Total interest = 11,400$ - 7,500$

Total interest = 3,900$

Since Christopher paid off the loan after 18 months instead of 24 months, he did not pay the full amount of interest he would have paid if he made all 24 payments. The unearned interest is therefore:

Unearned interest = Total interest - (Number of remaining payments / Total number of payments x Total interest)

Unearned interest = 3,900 - (6 / 24 x 3,900)

Unearned interest = 3,225$

Therefore, the amount of unearned interest is $3,225.

What is repay?

Part B:

To determine the amount needed to repay the loan using the Rule of 78, we need to calculate the proportion of the total interest that has been earned by the lender up to the point when Christopher repays the loan.

The Rule of 78 is a method of allocating interest charges based on the sum of the digits of the loan term. In this case, since the loan term is 24 months, the sum of the digits is:

1 + 2 + ... + 4 + 5 = 15

We can use this sum to calculate the proportion of the total interest earned by the lender up to the point when Christopher repays the loan:

Proportion of earned interest = (Number of payments made / Total number of payments) x (Sum of digits of loan term / Total sum of digits)

Proportion of earned interest = (18 / 24) x (15 / 120)

Proportion of earned interest = 0.09375

The total interest paid is 3,900$, so the amount needed to repay the loan using the Rule of 78 is:

Amount needed to repay loan = Amount borrowed + Total interest x Proportion of earned interest

Amount needed to repay loan = 7,500$ + 3,900$ x 0.09375

Amount needed to repay loan = 8,443.75$

Therefore, the amount needed to repay the loan using the Rule of 78 is $8,443.75.

Part C:

To support our answers to Part A and Part B, we calculated the total interest that Christopher would have paid if he made all 24 payments, which is 3,900$. We also calculated the unearned interest, which is the difference between the total interest and the interest that Christopher actually paid when he paid off the loan early.

Using the Rule of 78, we calculated the proportion of the total interest earned by the lender up to the point when Christopher repaid the loan, which is 0.09375. We then used this proportion to calculate the amount needed to repay the loan using the Rule of 78, which is $8,443.75.

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The value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.

Degree of freedom refers to the number of independent variables that can be varied in a statistical experiment or analysis. It is a measure of the flexibility of the experiment or analysis to accommodate new data or observations.

In this case, the degrees of freedom is 8. To find the t-value, the t-table must be consulted. The t-table is a chart of t-values for different degrees of freedom. The t-value is the value at which the area under the curve between 1 and 11 equals 0.95. The t-table is organized such that the rows represent the degrees of freedom and the columns represent the area under the curve. For example, if the degrees of freedom is 8 and the area under the curve is 0.95, the t-value can be found in the row for 8 degrees of freedom and the column for 0.95 area under the curve. The t-value from the t-table in this case is 1.86.

Therefore, the value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.

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complete ques is:

Consider data Y1​,Y2​,…Yn​ that is a random (i.e. independent) sample from a Normal distribution with unknown mean μ and known variance σ2. You wish to infer μ from the data using a Bayesian approach and select a prior on μthat is Normal with mean μ0​ and variance τ2. a. Derive the posterior distribution for μ. Since you should know the final result, credit will only be given for the derivation. b. Write down the posterior mean as a function of the posterior variance. Explain what happens to the posterior mean as a function of increasing n. c. Confirm your answer from part b) by plotting your results in R assuming μ0​=0,τ2=1,σ2=100, and with the data Yˉ=5 for n=1,10,100,1000.

In three years, the villa would cost roughly $18,375.64.

We can apply the compound interest formula if a villa's price is rising at a pace of 7% annually:

[tex]A = P(1 + r)^t[/tex]

The principal is the sum that was either lent or borrowed. It is the initial sum of money borrowed or lent in a loan, exclusive of interest or other costs. It serves as the baseline from which interest is determined. The total sum that must be repaid at the conclusion of the loan term is known as the principal amount. It is often referred to as the loan's face value or par value.

from the question:

We can apply the compound interest formula if a villa's price is rising at a pace of 7% annually:

[tex]A = P(1 + r)^t[/tex]

where A represents the overall sum, P represents the initial sum, r represents the annual interest rate in decimal form, and t is the number of years.

In this case, P = $15,000, r = 0.07, and t = 3. Plugging in these values, we get:

A = $15,000[tex](1 + 0.07)^3[/tex]

= $15,000[tex](1.07)^3[/tex]

= $15,000(1.225043)

= $18,375.64 (rounded to two decimal places)

As a result, the villa's price would be roughly $18,375.64 after three years.

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Answer:

P=(1100+1400)2

Step-by-step explanation:

Answer: there you go :)

$171.62 for social security.

$40.14 for Medicare.

Step-by-step explanation:

We have been given that Marika Perez’s gross biweekly pay is $2,768.

To find the amount deducted from her pay for social security tax, we will find 6.2% of her biweekly pay.

Therefore, $171.62 is deducted from Marika's biweekly pay.

Now let us find 1.45% of $2768 to find the amount of medicare deducted from her pay.

Therefore, an amount of $40.14 is deducted from Marika's biweekly pay for medicare.

The inequality and the shaded region are added as attachment

The given parameter from the question is represented as

0.4r ≤ 120 and r ≥ 4(360/5)

Evaluate the expression by products and quotients

So, the expression becomes

r ≤ 300 and r ≥ 288

When these inequalities are combined, we have the following compound expression of inequality

288 ≤ r ≤ 300

Next, we plot the graph of the inequality

The inequality is added as an attachment

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a) True. This is an example of sampling without replacement because once a person is selected for jury duty, they are no longer available for selection again.

b) 0.5238 is the probability.

a) Sampling without replacement is the technique of choosing a sample from a population without replacing the selected individuals in the population after each selection. In this case, once an eligible person is chosen, they cannot be chosen again.
Hence, the given statement is true.

b) We have to find the probability of all four of the excused jurors being women. We are picking four people out of 70 men and 80 women, or 150 people in total. Since we are dealing with independent events, we may use the multiplication principle for probabilities.
There are 80 women in the 150-person sample, so the probability of selecting one woman is 80/150.
After the first woman is selected, there are 79 women remaining in the 149-person sample, so the probability of selecting another woman is 79/149.
Similarly, the probabilities of selecting a third and fourth woman are 78/148 and 77/147, respectively.

Therefore, the probability that all four excused jurors are women is:
P(4 women) = (80/150) × (79/149) × (78/148) × (77/147)
P(4 women) = 0.5238 (rounded to four decimal places)
The probability that all four of the excused jurors are women is 0.5238.

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