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Volume of a prism: base area x height

Edge of each cube: 1 inch

Cubes used for the first layer: 42

Base area = 42 inches

height = 7 inches (or layers )

Volume = 42 x 7 = 294 cubic inches

Answer: -3x+y=-4

Step-by-step explanation:

Standard form is Ax+By=C. In y=Mx+b form, it would be y=3x-4. To put it into standard form you subtract 3x from both sides. So then you have -3x+y=-4.

The value of x in the parallel line is 11.

When parallel lines are cut with a transversal line, angle relationship are formed such as corresponding angles, alternate interior angles, alternate exterior angles, corresponding angles, vertically opposite angles etc.

Therefore, let's use the angle relationship to find the value of x .

Hence,

6x + 14 = 80(corresponding angles and vertically opposite angles)

6x + 14 = 80

subtract 14 from both sides of the equation

6x + 14 - 14 = 80 - 14

6x = 66

divide both sides of the equation by 6

x = 66 / 6

x = 11

Therefore,

x = 11

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The dimensions of the rectangular swimming pool are 25ft long 10ft wide and 8 feet deep.

A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height. Sometimes the cuboid shape is confused with a cube since it shares some properties of a cube, however, they are different from each other.

Volume of a cuboid  = Length(L) x Width(W) x Depth(d)

but L = 2.5w

2.5w x w x 8 = 2000

20W^2 = 2000

W^2 = 2000/20

W^2 = 100

W = \(\sqrt{100}\)

W = 10fft

L = 2.5W, but W = 10ft

L = 2.5 x 10

L = 25ft

In conclusion the length, width and depth are 25ft, 10ft, and 8ft respectively.

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Answer:

5

Step-by-step explanation:

A reciprocal is the inverse of a fraction.

To find it just flip the numerator and denominator.

1/5 becomes 5/1, or 5.

The calculated reciprocal of the number 1/5 is 5

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

Number = 1/5

By definition, the reciprocal of a number x is represebted as

reciprocal = 1/x

In this case,

x = 1/5

Substitute the known values in the above equation, so, we have the following representation

reciprocal = 1/(1/5)

Evaluate

reciprocal = 5

Hence, the reciprocal is 5

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The value for the number of red lights that Alice encounters are found.

X = no of red lights crossed by Alice.

X is Binomial distributed

In which  n=4, p=0.5, q = 0.5

Mean value is found by the formula,

Mean = np

Mean = 4×0.5

Mean = 2

And, variance = npq

Var = np(1-p)

Var = 4×0.5×0.5

Var = 1

PMF = ⁿCˣ0.5ˣ × 0.5 ⁽⁴⁻ˣ⁾

Thus, the value for  pmf, the mean, and the variance of the number of red lights that Alice encounters are found.

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Answer:

Step-by-step explanation:

How many carrots are in a can?  is that the question ?  :DDDDD

15/16   and  1/4 = 4/16 sooo

4*3 = 12

so three full servings  and one that is  3/4 full  

so 3

Answer:

Muercury 3

Venus 6

Mars 2

pluto 5

Jupiter 1

Nucleus4

Step-by-step explanation:

Answer

The third table has a gradient of 20, so third table is one of them.

The other one is the last case, For an hour, Fahim earning  $1010 so that is the rate per hour.  

Step-by-step explanation:

The points (2, 4) and (-5, 3) lie on the line y - 4 = (1/3)(x + 2) and the graph is drawn below. Then the correct option is C.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y - 4 = (1/3)(x + 2)

At x = - 2, the value of y is given as,

y - 4 = (1/3)(- 2 + 2)

y = 4

At x = - 5, then we have

y - 4 = (1/3)(- 5 + 2)

y - 4 = - 1

y = 3

The focuses (2, 4) and (- 5, 3) lie on the line y - 4 = (1/3)(x + 2), and the diagram is drawn beneath. Then the right choice is C.

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Answer:

Step-by-step explanation:

yoooooo

The uniform continuous probability for the interval (25 < x < 45) within the uniform distribution U(15, 65) can be found by calculating the proportion of the total range that falls within that interval.

To calculate the probability, we need to determine the length of the interval (45 - 25) and divide it by the length of the entire range (65 - 15).

Length of the interval: 45 - 25 = 20

Length of the entire range: 65 - 15 = 50

Now, we divide the length of the interval by the length of the entire range to obtain the probability:

Probability = (Length of interval) / (Length of entire range) = 20 / 50 = 0.4

Therefore, the uniform continuous probability for p(25 < x < 45) within the uniform distribution U(15, 65) is 0.4, rounded to one decimal place.

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∠HGF ∠EGF

Hope this helps! :)

Could you please provide the units

Answer:

1.  10√3

2. -√5

3. 21√3 -9√5

4. 12√7-√11

5. 8√5-3(√5*√4) = 8√5- (3*2)√5= 2√5

6. √5*√4 -√5= 2√5-√5= √5

7. 3√5*√9 +√5*√4 -√49*√5 = 15√5+2√5-7√5= 10√5

8. √6*√4 - √6*√9 + √16*√6= 2√6-3√6+4√6= 3√6

Hope it helps you :)

Answer:

CBA = 53°

DBC = 39°

Step-by-step explanation:

You have 2 angles, CBA and DBC.

Together, these form the angle DBA. (See attached image)

We know the following about the 2 angles:

CBA = 8x - 3

DBC = 5x + 4

Like we said, both of these together form the angle DBA. Thus:

DBA = CBA + DBC

Let's put in the values we know, 8x-3, 5x+4, instead of CBA and DBC:

DBA = 8x - 3 + 5x + 4

DBA = 13x - 3 + 4

DBA = 13x + 1

We also know that:

DBA = 92 (from the question)

Let's set our expression 13x + 1 equal to 92.

DBA = 13x + 1

DBA = 92

13x + 1 = 92

Subtract 1 from both sides:

13x = 91

Divide both sides by 13:

x = 91 / 13

x = 7

Now that we know x, we can find what CBA and DBC are.

CBA = 8x - 3

Replace x with 7:

CBA = 8*7 - 3

CBA = 56 - 3

CBA = 53

DBC = 5x + 4

Replace x with 7:

DBC = 5*7 + 4

DBC = 35 + 4

DBC = 39

Answer:

CBA = 53°

DBC = 39°

the base of the triangular window is 24 feet and the height is 10 feet.

Let's denote the height of the triangular window as h feet. According to the given information, the area of the window is 120 square feet.

The formula to calculate the area of a triangle is:

Area = (1/2) × base × height

In this case, we can write the equation as:

120 = (1/2) × base × h

Now, we are also given that the base of the window is 4 feet more than twice the height. So we can express the base as:

base = 2h + 4

Substituting this expression for the base into the area equation, we have:

120 = (1/2) × (2h + 4) × h

Now we can solve this equation for the height.

Multiplying both sides of the equation by 2 to remove the fraction:

240 = (2h + 4) × h

Expanding the right-hand side:

240 = 2h² + 4h

Rearranging the equation and setting it equal to zero:

2h² + 4h - 240 = 0

Now we can solve this quadratic equation. Factoring out a 2:

2(h² + 2h - 120) = 0

Factoring the quadratic expression inside the parentheses:

2(h + 12)(h - 10) = 0

Setting each factor equal to zero:

h + 12 = 0   or   h - 10 = 0

Solving these equations, we get:

h = -12   or   h = 10

Since height cannot be negative in this context, we discard the negative value. Therefore, the height of the triangular window is h = 10 feet.

Substituting the height value back into the expression for the base:

base = 2h + 4

    = 2(10) + 4

    = 20 + 4

    = 24

Therefore, the base of the triangular window is 24 feet and the height is 10 feet.

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Answer:

73.198

Step-by-step explanation:

basically I'm not gonna explain this but it wants me to write 20 words so imma write this so I can post thjs

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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The observed allele frequencies for the T102C locus are as follows: T allele frequency = 0.388 and C allele frequency = 0.612.


To calculate the observed allele frequencies, we divide the number of occurrences of each allele by the total number of alleles observed.

In this case, the T allele is observed in 108 TT genotypes and 194 TC genotypes, giving a total of 108 + 194 = 302 T alleles. Similarly, the C allele is observed in 194 TC genotypes and 48 CC genotypes, giving a total of 194 + 48 = 242 C alleles.

To calculate the T allele frequency, we divide the number of T alleles by the total number of alleles: 302 T alleles / (302 T alleles + 242 C alleles) = 0.388 (or approximately 0.39).

Similarly, the C allele frequency is calculated as: 242 C alleles / (302 T alleles + 242 C alleles) = 0.612 (or approximately 0.61).

Therefore, the observed allele frequencies for the T102C locus are T allele frequency = 0.388 and C allele frequency = 0.612.

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Answer:

60

Step-by-step explanation:

D

Answer:

c

Step-by-step explanation:

the graph shows a constant speed an no change in distance

Between 10:00 and 10:30, there is a 0.333 percent chance that the switchboard will field more than 9 calls but fewer than 18 calls.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Time = 30 min (as 10:00 to 10:30)

Total calls = 9+18 =27

Probability receive more than 9 calls but fewer than 18 calls

p(9 < x > 18) = { 10, 11, 12, 13, 14, 15, 16, 17, 18}  = 9 (all possibilities)

Total Probability = (likely event / total outcomes)

p(9 < x > 18) = (9/27)

p(9 < x > 18) = 1/3

p(9 < x > 18) = 0.333

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Answer:

x= {0, 7}

Step-by-step explanation:

Answer:

semoga jawapan ini dapat membantu

The sentence can be turned to the equation;

15.00r+20.00(r−3)=500.00

We have to read the sentence carefully and identify the quantities or variables involved.

We are told that a  barber offers two options at his barbershop; a $15 regular haircut and a $20 deluxe haircut.

Then  On a certain day the barber gave r regular haircuts and 3 fewer deluxe haircuts than regular haircuts. He earned $500 total from the two types of haircuts.

It then follows that the correct equation is 15.00r+20.00(r−3)=500.00

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Missing parts;

A barber offers two options at his barbershop: a $15.00 regular haircut and a $20.00 deluxe haircut. On a certain day, the barber gave r regular haircuts and 3 fewer deluxe haircuts than regular haircuts. He earned $500.00 total from the two types of haircuts. Which of the following equations best models this situation?

Answer Choices:

A. 15.00r+20.00(r−3)=500.00

B. 15.00r+20.00(r+3)=500.00

C. 15.00(r−3)+20.00r=500.00

D. 15.00(r+3)+20.00r=500.00

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

If f(2) = 1 and the tangent line at x has slope (x − 1)ex2 − 2x. f(x) = ((x^2 - 2x + 1)/2)e^(x^2 - 2x).

To find f(x), we'll first integrate the given slope function to obtain the original function. The slope of the tangent line is given as (x - 1)e^(x^2 - 2x).

Let F'(x) = (x - 1)e^(x^2 - 2x). To find f(x), we need to integrate F'(x) with respect to x:

∫(x - 1)e^(x^2 - 2x) dx

Now, we can use substitution. Let u = x^2 - 2x, then du = (2x - 2) dx. Therefore, the integral becomes:

∫((u + 1)/2)e^u du

Now, we can integrate by parts. Let v = e^u, then dv = e^u du. Let w = (u + 1)/2, then dw = 1/2 du. Using integration by parts formula:

∫w dv = wv - ∫v dw

∫(u + 1)/2 * e^u du = ((u + 1)/2)e^u - ∫(1/2)e^u du

Now integrate the remaining part:

∫(1/2)e^u du = (1/2)e^u + C

Substituting back:

f(x) = ((x^2 - 2x + 1)/2)e^(x^2 - 2x) + C

Now, use the given condition f(2) = 1:

1 = ((2^2 - 2*2 + 1)/2)e^(2^2 - 2*2) + C

1 = (1)e^0 + C

C = 0

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∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Given:

Three lines AD, CF, and BE are intersecting each other at the midpoint O.

To prove:

∠CFA ≅ ∠EDA

Proof:

Given that AD, CF, and BE intersect at the midpoint O.

By definition of a midpoint, OA ≅ OD, OB ≅ OE.

OA = OD and OB = OE.

Triangle OAD ≅ Triangle OBE (By Side-Side-Side congruence).

∠OAD ≅ ∠OBE (By Corresponding Parts of Congruent Triangles are Congruent).

∠CFA and ∠EDA are vertical angles.

∠OAD ≅ ∠CFA and ∠OBE ≅ ∠EDA (By Vertical Angles are Congruent).

Therefore, ∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Hence, it is proven that ∠CFA ≅ ∠EDA.

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