prove this geometry

given: trapezoid abcd where ba is congruent to cd angle abc is congruent to angle dcb

prove bd is congruent to ac

The worker will earn 24,000 naira in 1/2 year

A worker earns 4000 naira per month

The amount he earns in 1/2 year can be calculated as follows

1/2 of a year is 6 months

The amount of money the worker will earn in six months can be calculated as follows

= 4,000 × 6

= 24,000

Hence the worker will earn 24,000 naira in 1/2 of a year(six months)

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222 people were influenced by brand.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To determine how many people were influenced by brand, we need to add up the number of people who said "brand" as one of their influencing factors. However, we need to be careful not to double-count those who selected multiple factors.

Let's start by creating a diagram of the data:

         | Color | Size | Brand | Total

Only      |   5   |  8   |   16  |   29

Color/Size|  20   |  0   |   42  |   62

Size/Brand|   0   |  53  |   42  |   95

All Three |   0   |  0   |  102  |  102

None      |  20   |  20  |   20  |   60

Total     |  45   |  81  |  222  |  348

From this table, we can see that 222 people said that brand influenced their choice of cell phone.

Therefore, 222 people were influenced by brand.

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The graph of the point is on the image at the end.

A coordinate plane has two axes, one is horizontal and the other is vertical.

A general point (x, y) has the value "x" in the horizontal axis and "y" in the vertical one, then to graph (-312, 434 ) in a coordinate plane, you need to find -312 in the horizontal axis and 434 in the vertical one.

The graph of the point is on the image at the end.

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The measures of the angles are JKN = 27 degrees and JNK = 126

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The rectangle

On the rectangle, we have

JKN = NJK

Using the above as a guide, we have the following:

JKN = 27 degrees

Next, we use the sum of angles in a triangle theorem

The sum of angles in a triangle is 180

Mathematically, this is represented as

J + N + K = 180

So, we have the following representation

JNK = 180 - 27 * 2

Evaluate

JNK = 126

Hence, the measure of the angle JNK is 126 degrees

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a) The correct null and alternative hypotheses are: given in option A:
H₀: Pkids = Padults

Ha: Pkids < Padults

b) the p-value is 0.004 (rounded to three significant figures).

a) The correct null and alternative hypotheses are:

H₀: Pkids = Padults (The proportion of kids who eat cereal for breakfast is equal to the proportion of adults who eat cereal for breakfast)

Ha: Pkids < Padults (The proportion of kids who eat cereal for breakfast is less than the proportion of adults who eat cereal for breakfast)

b) To test this claim, we can use a two-sample z-test for proportions. We calculate the test statistic as follows:

z = (phat1 - phat2) / √(p*(1-p)*(1/n1 + 1/n2))

where phat1 and phat2 are the sample proportions, n1 and n2 are the sample sizes, and p is the pooled proportion. The pooled proportion is calculated as:

p = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of successes in each sample.

Using the given data, we have:

phat1 = 70/95 = 0.737

phat2 = 35/58 = 0.603

n1 = 95

n2 = 58

x1 = 70

x2 = 35

p = (70 + 35) / (95 + 58)

= 0.680

Then, the test statistic is:

z = (0.737 - 0.603) / √(0.680*(1-0.680)*(1/95 + 1/58))

= 2.62

Using a standard normal distribution table or calculator, we find the p-value associated with a z-score of 2.62 is approximately 0.004.

Therefore, the p-value is 0.004 (rounded to three significant figures).

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the proportion of kids who eat cereal for breakfast is less than the proportion of adults who eat cereal for breakfast.

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Full Question:

Cereal for Breakfast. A parent claims that kids eat cereal for breakfast more often than adults. A statistics-loving friend of the parent does some internet research and finds the following polling data. Of 95 kids polled, 70 of them say cereal is their most common breakfast. Of 58 adults polled, 35 of them say cereal is their most common breakfast. Test the parent's claim using these data.

a) Select the correct null and alternative hypotheses

H₀: Pkids = Padults

Ha: Pkids < Padults

H₀: Pkids = Padults

Hat Pkids ≠ Padults

H₀: Pkids = Padults

Ha: Pkids > Padults

b) Find the p-value (round to three significant figures).

Answer:

c = 8t + 2.5

Step-by-step explanation:

The total cost c of buying t tickets is given by:

c = 8t + 2.5

Answer:

The total cost of buying t tickets can be represented by the equation:

c = 8t + 2.50

Where:

c is the total cost in dollars

t is the number of tickets bought

Answer:

The product of the matrices A and X is the identity matrix. Therefore, X and A are inverses of each other.

Step-by-step explanation:

Kevin will have 6 ounces of fruit snack left over after filling the 4 pound containers.

There are several systems of measurement units, including the International System of Units (SI), the United States customary system, and the British imperial system. The SI is the most widely used system and is based on seven base units, including the meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity).

To determine how many containers Kevin can fill, we need to first calculate the total weight of the fruit snack.

Total weight of the fruit snack = Weight of dried apples + Weight of dried cranberries

= 48 ounces + 22 ounces

= 70 ounces

Since there are 16 ounces in 1 pound, we can convert the total weight to pounds as follows:

Total weight in pounds = 70 ounces ÷ 16 ounces/pound

= 4.375 pounds

Therefore, Kevin can fill 4 pound containers with fruit snack, with 0.375 pounds of fruit snack left over.

To determine if any fruit snack will be left over, we need to convert the remaining weight of 0.375 pounds back to ounces:

0.375 pounds × 16 ounces/pound = 6 ounces

Therefore, Kevin will have 6 ounces of fruit snack left over after filling the 4 pound containers.

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The probability that a randomly selected person from the group is a Toronto Blue Jays fan is 11/30.

Probability refers to the chance or likelihood that an expected outcome, event, or success occurs when there are many possible outcomes, events, or successes.

Probability is a fractional value that lies between one and zero depending on the degree of certainty.

Probabilities can be expressed as decimals, fractions, or percentages.

The total number of people who gathered to watch the baseball game = 30

The number of Toronto Blue Jays fans = 11

Thus, the probability of selecting a Toronto Blue Jay fan from the 30 spectators is 11/30.

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The quadrilateral is most specifically a D. square, because C. all sides are congruent.

What is a square?

A quadrilateral with four equal edges is called a square. There are numerous items in our environment that have a square form. Equal sides and interior angles that are both 90 degrees distinguish each square form.

A square is a quadrilateral where all sides are congruent and all angles are right angles.

This matches the given description of the figure with 4 vertices, where the diagonal angles are same and all the sides are equal.

Therefore, the correct option for the first blank is D, and the correct options for the second blank is C.

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Answer:

The quadrilateral is most specifically a rhombus because all sides are congruent.

Step-by-step explanation:

From inspection of the given quadrilateral, we can see that:

(This is denoted by the same number of tick marks on each congruent line segment and each congruent angle).

All sides of a square and a rectangle meet at right angles, i.e. their interior angles are congruent. Since the interior angles of the given quadrilateral are not all equal, the figure cannot be a square or a rectangle.

All sides of a rhombus are equal in length, and its opposite angles are congruent. This description matches the given shape. Therefore, the quadrilateral is a rhombus.

the amount Mrs. Lee buys in pounds of ham is given by y = 2x - 2.5.

Why it is and what is pound ?

If Mrs. Kim buys 2x pounds of ham, then Mrs. Lee buys 2.5 less pounds, or (2x - 2.5) pounds of ham.

We are asked to express the amount Mrs. Lee buys in terms of x, so we can write:

y = 2x - 2.5

Therefore, the amount Mrs. Lee buys in pounds of ham is given by y = 2x - 2.5.

Pound is a unit of measurement used to quantify weight or mass. It is abbreviated as "lb" or "lbs" and is commonly used in the United States and other countries. One pound is approximately 0.45 kilograms.

The pound is defined as exactly 0.45359237 kilograms, which is based on the international avoirdupois pound. In everyday use, the pound is often used to measure the weight of objects such as food, animals, and people.

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Answer:hunger

Step-by-step explanation:

i hungry

The way we can find the pencil Dan has in total is 16+5

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

This word problem are interpreted to mathematical equations.

San has 16 pencils with him before,

Quentin gives him more 5 pencils

then the total pencil Dan will have is obtained by adding all the pencils together,

= 16+5

= 21 pencils

therefore the total number of pencil is found by 16+5 = 21

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Answer:

No, lines of latitude on a globe are not examples of lines in elliptic geometry. Elliptic geometry is a non-Euclidean geometry in which there are no parallel lines, and the sum of the angles in a triangle is greater than 180 degrees. However, lines of latitude on a globe are examples of lines in spherical geometry, which is a type of elliptic geometry. In spherical geometry, lines of latitude are great circles, which are the largest circles that can be drawn on a sphere and are analogous to the equator on Earth. Unlike lines in Euclidean geometry, great circles on a sphere do not maintain a constant distance from each other and intersect at two points on the sphere.

Step-by-step explanation:

Answer:

We can start by dividing the total amount of fertilizer by the number of acres:

162 pounds / 4 acres = 40.5 pounds per acre

Therefore, the farmer uses 40.5 pounds of fertilizer on each acre of crops.

Step-by-step explanation:

A. The price of the bond is $556.25.

B. The yield to maturity expected by investors is 20.36%.

Yield to maturity (YTM) is the total rate of return that will have been earned by a bond when it makes all interest payments and repays the original principal.

here, we have,

A. The price of the bond is calculated using the formula:

P = C × (1 − (1 + YTM/2)−2T ) ÷ (YTM/2) + (1 + YTM/2)−2T

Here, C is the coupon payment, YTM is the yield to maturity and T is the time to maturity in years.

Face value = $1,000

YTM = 8.2%

Time to maturity = 7 years

Coupon payment = 8.2% × $1,000 = $82

Substituting these values in the formula, we get:

P = $82 × (1 − (1 + 0.082/2)−14 ) ÷ (0.082/2) + (1 + 0.082/2)−14

P = $82 × (1 − 0.6774) ÷ 0.041 + 0.6774

P = $556.25

B. The yield to maturity expected by investors is calculated using the formula:

YTM = 2 × (C × (1 + YTM/2)−2T + (FV − P) × (1 + YTM/2)−2T ) ÷ P

Here, C is the coupon payment, YTM is the yield to maturity, FV is the face value of the bond and P is the price of the bond.

Expected face value at maturity = 85% × $1,000 = $850

Substituting these values in the formula, we get:

YTM = 2 × ($82 × (1 + YTM/2)−14 + ($850 − $556.25) × (1 + YTM/2)−14 ) ÷ $556.25

YTM = 2 × ($82 × (1 + YTM/2)−14 + ($293.75) × (1 + YTM/2)−14 ) ÷ $556.25

YTM = 2 × ($82 × 0.6774 + ($293.75) × 0.6774) ÷ $556.25

YTM = 2 × ($55.35 + ($198.57) ) ÷ $556.25

YTM = 2 × $253.92 ÷ $556.25

YTM = 0.2036 = 20.36%

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The statement that is not correct is FG/RS = EF/OS, the correct option is C.

A side of one triangle = k times corresponding side of its similar triangle

where k is the scale factor, constant for one pair of similar triangles. Now when we will take their ratio, the value of k cancels out, leaving no difference between first triangle or second triangle, but only caring if they are similar or not(which depends on angles).

Thus, the trigonometric functions depend only on angles.

We are given that;

Triangles EFG and QRS are similar

Now,

Option A states that EF/QR = CE/SQ, which is true by the definition of similarity of triangles.

Option B states that FG/RS = EG/QS, which is also true by the definition of similarity of triangles.

Option D states that 4GE/SQ = FE/RQ, which is also true as corresponding sides are proportional.

However, option C states that FG/RS = EF/OS, which is not necessarily true. There is no direct relationship between side OS and triangle EFG, so the ratio FG/RS cannot be equated to the ratio EF/OS.

Therefore, by the given similar triangles answer will be FG/RS = EF/OS.

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Even though the triangles are all different sizes,the decimal for each ratio are equal.

What is ratio ?

Ratios are commonly used in many different fields, including finance, engineering, and science. They are used to compare quantities or values that are not necessarily in the same units or are not directly comparable.

If the ratios of the corresponding sides of different triangles are equal, then the triangles are said to be similar. In this case, if the ratios of the sides of the different triangles are equal and result in the same decimal value, then it means that the triangles are similar to each other.

When two triangles are similar, it means that their corresponding angles are equal, and the ratios of their corresponding sides are also equal. This is known as the "angle-angle" or "AA" similarity criterion.

Therefore, if the ratios of the sides of different triangles are equal.

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Answer:

slope = 1/3

Step-by-step explanation:

9x-3y=81

-9x       -9x

3y/3= -9x + 81/3

y = -3x +27

is perpendicular to...

y = 1/3x + 27

Answer: im sorry you got scamed :(  but heres the answer the answer is C! Min: 30, Q1: 44, Median: 60, Q3: 70, Max: 82

Step-by-step explanation:

How do i know this? well if you look at the box plot it shows you that! it shows a tick on 30, 44, 60, 70 and 82 to its corresponding quartiles. and answer C is the only one that shows this. therefore the answer is C!

Answer: 6.5

Step-by-step explanation:

[tex]|-6.5| = 6.5[/tex]

_________

Answer:

Step-by-step explanation:

To calculate the present value (PV) and future value (FV) of the cash flow stream, we can use the following steps:

Calculate the present value of each cash flow using the formula:

PV = CF / (1 + r)^n

where CF is the cash flow, r is the annual interest rate, and n is the number of years until the cash flow is received.

For the first three cash flows of $150 at the end of each of the next 3 years, assuming a starting point of Year 0, we have:

PV1 = $150 / (1 + 0.11)^1 = $134.59 (Year 1)

PV2 = $150 / (1 + 0.11)^2 = $120.75 (Year 2)

PV3 = $150 / (1 + 0.11)^3 = $107.99 (Year 3)

For the cash flow of $250 at the end of Year 4:

PV4 = $250 / (1 + 0.11)^4 = $165.14

For the cash flow of $300 at the end of Year 5:

PV5 = $300 / (1 + 0.11)^5 = $179.34

For the cash flow of $500 at the end of Year 6:

PV6 = $500 / (1 + 0.11)^6 = $277.12

Add up the present values of each cash flow to find the present value of the entire stream:

PV = PV1 + PV2 + PV3 + PV4 + PV5 + PV6

PV = $134.59 + $120.75 + $107.99 + $165.14 + $179.34 + $277.12

PV = $985.93

Therefore, the present value of the cash flow stream is $985.93.

To find the future value of the cash flow stream, we can simply add up the cash flows and then apply the future value formula:

FV = CF x [(1 + r)^n - 1] / r

where CF is the sum of the cash flows, r is the annual interest rate, and n is the number of years from the present until the future value is calculated.

CF = $150 x 3 + $250 + $300 + $500 = $1,100

n = 6 (assuming a starting point of Year 0)

FV = $1,100 x [(1 + 0.11)^6 - 1] / 0.11

FV = $2,525.72

Therefore, the future value of the cash flow stream is $2,525.72.

The ratio of quarters to the total number of coins is 25:100, or simplified to 1:4.

What is the ratio and proportion ?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls).

To find the ratio of quarters to the total number of coins, we need to first calculate the total number of coins.

Total number of coins = number of quarters + number of dimes + number of pennies + number of nickels

Total number of coins = 25 + 20 + 50 + 5

Total number of coins = 100

Therefore, the total number of coins is 100.

The ratio of quarters to the total number of coins is:

Quarters : Total number of coins

= 25 : 100

= 1 : 4

Hence, the answer is option 3. 1/4.

Therefore, the ratio of quarters to the total number of coins is 25:100, or simplified to 1:4.

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Answer: [tex]$m=-\frac{1}{22}$[/tex]   [tex]$b=\frac{15}{22}$[/tex]

Step-by-step explanation:

To find the equation of the tangent line to the curve [tex]$xy^3+xy= 14$[/tex] at the point [tex]$(7,1)$[/tex] we need to first find the derivative of the equation with respect to x using implicit differentiation.

Taking the derivative of both sides with respect to x:

[tex]$\frac{d}{dx}(xy^3+xy)=\frac{d}{dx}(14)$[/tex]

Using the product rule and chain rule:

[tex]$y^3+x(3y^2\frac{dy}{dx}+y)=0$[/tex]

Simplifying and solving for [tex]$\frac{dy}{dx}$[/tex]

[tex]$\frac{dy}{dx}=-\frac{y}{3y^2+1}$[/tex]

Now we can substitute x=7 and y=1 into this equation to find the slope of the tangent line at the point (7,1):

[tex]$m=\left.-\frac{y}{3y^2+1}\right|_{(7,1)}=-\frac{1}{22}$[/tex]

So the slope of the tangent line is [tex]$-\frac{1}{22}$[/tex]

To find the y-intercept, we can use the point-slope form of the equation of a line:

[tex]$y-1 = m(x-7)$[/tex]

[tex]$y=mx+(1-7m)$[/tex]

Therefore, the equation of the tangent line to the curve [tex]$xy^3+xy=14$[/tex] at the point (7,1) can be written as:

[tex]$y=-\frac{1}{22}x+\frac{15}{22}$[/tex]

So [tex]$m=-\frac{1}{22}$[/tex] and [tex]$b=\frac{15}{22}$[/tex]

The missing angles inscribed in the circle are

The angles are calculated using the inscribed angle theorem

Inscribed Angle Theorem: The measure of an inscribed angle is half the measure of the intercepted arc.

This is used as follows

∠ C = 52/2 degrees

∠ C = 26 degrees

∠ C = ∠ B = 26 degrees inscribed angle subtended by same arc are equal

∠ BSD + ∠ D + B = 180 degrees sum of angles in a triangle

∠ BSD + 57 + 26 = 180

∠ BSD = 180 - 57 - 26

∠ BSD = 97 degrees

∠ CSE = ∠ BSD vertical angles

∠ CSE = 97 degrees

∠ E = ∠ B = 57 degrees inscribed angle subtended by same arc are equal

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Answer:

Alan had 272 cards initially and Ben had 88 cards initially.

Step-by-step explanation:

Let's start by assuming that Alan had x cards and Ben had y cards initially. We know that the sum of their cards is 360, so:

x + y = 360

In the first game, Alan lost 2/5 of his cards to Ben, so he gave away (2/5)x cards to Ben. Therefore, he was left with:

(3/5)x cards

Ben received (2/5)x cards from Alan and had y cards initially, so he had:

y + (2/5)x

cards after the first game.

In the second game, Alan won 1/4 of Ben's cards, so he received (1/4)(y + (2/5)x) cards. Therefore, he had:

(3/5)x + (1/4)(y + (2/5)x)

cards after the second game.

In the third game, Alan lost 1/6 of his cards to Ben, so he gave away (1/6)(3/5)x cards to Ben. Therefore, he was left with:

(2/3)(3/5)x = (2/5)x

cards.

Ben received (1/6)(3/5)x cards from Alan in the third game, and he had y + (2/5)x cards after the first game. Therefore, he had:

y + (2/5)x + (1/6)(3/5)x = y + (9/25)x

cards after the third game.

Since both boys ended up with the same number of cards, we can set the expressions for their final card counts equal to each other:

(3/5)x + (1/4)(y + (2/5)x) = y + (9/25)x

Multiplying both sides by 100 to get rid of the fractions, we get:

60x + 25y + 50x = 100y + 36x

Simplifying, we get:

24x = 75y

Since x + y = 360, we can use this equation to solve for one of the variables in terms of the other:

x = 360 - y

Substituting into the equation we just obtained, we get:

24(360 - y) = 75y

Simplifying, we get:

8640 - 24y = 75y

99y = 8640

y = 87.27

Since y must be a whole number (since it represents the number of cards that Ben had initially), we can round it up to 88. Substituting into the equation x + y = 360, we get:

x + 88 = 360

x = 272

Therefore, Alan had 272 cards initially and Ben had 88 cards initially.

To find the initial number of game cards Alan and Ben had, we can set up an equation and solve for a variable. The equation involves using the information about the games played and the number of cards lost and gained by Alan. The solution will give us the initial numbers of cards for both boys.

To solve this problem, let's assume that Alan had x cards and Ben had y cards at the beginning. We are given that Alan lost 2/5 of his cards to Ben in the first game, so he had (3/5)x cards left and Ben had y + (2/5)x cards. In the second game, Alan won 1/4 of Ben's cards, so he gained (1/4)(y + (2/5)x) cards, leaving him with (3/5)x + (1/4)(y + (2/5)x) cards. In the last game, Alan lost 1/6 of his cards to Ben, so he had (5/6)((3/5)x + (1/4)(y + (2/5)x)) cards left. Since both boys had the same number of cards in the end, we can set up the equation: (5/6)((3/5)x + (1/4)(y + (2/5)x)) = y + (2/5)x. After simplifying and solving for y in terms of x, we can substitute back into the equation to find the value of x.

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Answer:

Step-by-step explanation:

To solve the differential equation x^2y'' − 3xy' + 3y = x^4e^x using variation of parameters, we can follow these steps:

Step 1: Find the complementary solution y_c by solving the homogeneous equation:

x^2y'' − 3xy' + 3y = 0

The characteristic equation is r(r-1) - 3r + 3 = 0, which simplifies to r^2 - 4r + 3 = 0. Factoring, we get (r-1)(r-3) = 0, so the roots are r=1 and r=3. Therefore, the complementary solution is:

y_c = c1x + c2x^3

where c1 and c2 are arbitrary constants.

Step 2: Find the particular solution y_p using variation of parameters. We assume that the particular solution has the form:

y_p = u1(x)*y1(x) + u2(x)*y2(x)

where y1 and y2 are solutions to the homogeneous equation (in this case, y1=x and y2=x^3) and u1 and u2 are functions to be determined.

We need to find the derivatives of y1 and y2:

y1' = 1, y1'' = 0

y2' = 3x^2, y2'' = 6x

Substituting into the differential equation and simplifying, we get:

x^2(u1''y1 + u2''y2) + x(u1'y1 + u2'y2) = x^4e^x

Plugging in y1 and y2 and simplifying, we get:

x^2(u1''*x + u2''*x^3) + x(u1'*1 + u2'*3x^2) = x^4e^x

We can write this equation in matrix form as:

[x^2x, x^2x^3] * [u1'', u2''] + [x1, x3x^2] * [u1', u2'] = [0, x^4e^x]

Taking the determinant of the coefficient matrix [x^2x, x^2x^3; x1, x3x^2], we get:

(x^2x)(x3x^2) - (x^2x^3)*x = 2x^4

Therefore, the inverse of the coefficient matrix is:

[3x, -x^3] / (2x^4)

Multiplying by the column vector [0, x^4e^x] gives:

[u1', u2'] = [3x, -x^3] * (1/(2x^4)) * [0, x^4e^x]

Simplifying, we get:

u1' = (3/2)*e^(-x), u2' = -(1/2)xe^(-x)

Integrating u1' and u2' with respect to x, we get:

u1 = -(3/2)*e^(-x), u2 = -(1/2)*xe^(-x) + C

where C is an arbitrary constant.

Therefore, the particular solution is:

y_p = -(3/2)xe^(-x) + Cx^3e^(-x)

where C is an arbitrary constant.

Step 3: The general solution of the differential equation is the sum of the complementary solution and the particular solution:

y = y_c + y_p

Answer:

8

Step-by-step explanation:

4 + 2 (5 - 3) = 8

hope this helps :))