pls help ASAP !! 30 PTS

The values of {x} and {y} for which both the equations are true are {x} = 3 and {y} = 1.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given is the system of simultaneous equations as -

{y} = -{2/3}x + 3

{y} = 2x - 5

Refer to the graph of the equations attached. The value of {x} and {y} for which both the equations are true is given by the point of intersection of both lines.

Therefore, the values of {x} and {y} for which both the equations are true are {x} = 3 and {y} = 1.

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The total length of the hose, in yards, is 12 11/12 yards.

To find the total length of the hose, we need to add the lengths of the two hoses. The first hose is 5 5/6 yards long, and the second hose is 6 3/4 yards long.

To add these two lengths, we need to find a common denominator for the fractions. The common denominator for 6 and 4 is 12. So, we convert the mixed numbers to improper fractions:

5 5/6 = (6 * 5 + 5) / 6 = 35/6

6 3/4 = (4 * 6 + 3) / 4 = 27/4

Now, we can add the two fractions: 35/6 + 27/4

To add these fractions, we need a common denominator, which is 12. We convert both fractions to have a denominator of 12:

35/6 = (35/6) * (2/2) = 70/12

27/4 = (27/4) * (3/3) = 81/12

Now, we can add the fractions: 70/12 + 81/12 = 151/12

The resulting fraction, 151/12, can be simpified to a mixed number: 151/12 = 12 11/12

Therefore, the total length of the hose, in yards, is 12 11/12 yards.

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Answer:

3, 5

Step-by-step explanation:

Answer:

52 units²

Step-by-step explanation:

A = L × W

Area = Length × Width

First find the total area: 44

Half that to find the total left side that is shaded: 22

Find the bottom right side, imagine it is a seperate shape. It would be 4 × 2 = 8. 44 + 8 = 52.

- Educator

A statistician would reply that in order to determine if the generic drug is less effective than the name-brand drug, a hypothesis test needs to be conducted.

The null hypothesis (H0) would be that there is no difference in the average blood pressure reduction between the two drugs, while the alternative hypothesis (H1) would be that the name-brand drug has a higher average reduction in blood pressure than the generic drug.

To test these hypotheses, a t-test would be appropriate since we have two independent samples (control and treatment groups) with known means, standard deviations, and sample sizes. The t-test will provide a p-value, which can be compared to a chosen significance level (e.g., α = 0.05).

If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference in the average blood pressure reduction between the two drugs. If the p-value is greater than the significance level, we fail to reject the null hypothesis, meaning we do not have enough evidence to claim that the name-brand drug is more effective than the generic drug.

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Using Pascal's triangle the expansion of the expression \((5x+5)^3\) is \(125x^3+375x^2+375x+125\).

What is Pascal's triangle?

The triangle can be used to calculate the coefficients of the expansion of  \((a+b)^n\) by taking the exponent n and adding 1. The coefficient will correspond with line n+1 of the triangle.

Here for \((5x+5)^3\) , n= 3 so the coefficient of the expansion will correspond with line 4.

The expansion follow the rule ,

\((a+b)^n=c_{0}a^nb^0+c_{1}a^{n-1}b^1+c_{n-1}a^1b^{n-1}+c_{n}a^0b^n\)

The values of the coefficients, from the triangle, are 1-3-3-1.

=> \(1a^3b^0+3a^2b+3a^1b^2+1a^0b^3\)

Here substitute a=5x and b=5 then,

=> \(1(5x)^35^0+3(5x)^25+3(5x)^25^2+1(5x)^15^3\)

=> \(125x^3+375x^2+375x+125\)

Hence the expansion of the expression \((5x+5)^3\) is \(125x^3+375x^2+375x+125\).

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The probability that all of them get the same number is 1/36.

Given :

Three people are asked to throw a fair die.

Probability :

Probability is a branch of mathematics that deals with the occurrence of a random event.

In one dice probable outcomes 1, 2, 3, 4, 5 and 6

Total out comes in three dice = ( 6 * 6 * 6 = 216 )

Probability of getting 1 = 1/216

Similarly for 2, 3, 4, 5 and 6

Probability of getting same number = 6 * 1/6 * 1/6 * 1/6

= 6*1/6 * 1 * 1 / 6 * 6

= 6/6 * 1/36

= 1 * 1/36

= 1/36

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If a cartoon of 2 dozen eggs includes 3 with cracks, then the number of eggs without cracks in 6 dozen eggs can be expected to be 63.

A dozen abbreviated as doz is a batch of 12. So in this situation, one dozen refers to 12 eggs. Therefore the number of eggs in 2 dozen will be equal to,

1 dozen = 12 eggs

2 dozen = 12x2= 24 eggs.

Therefore, a cartoon of 24 eggs includes 3 with cracks.

Similarly, 6 dozen is equal to,

1 dozen = 12 eggs

6 dozen = 12 x 6 = 72 eggs

We can determine the number of eggs with cracks by using an algebraic expression,

24 eggs include 3 eggs with cracks

72 eggs include: x eggs with cracks

x = 72×3 ÷ 24

x = 216 ÷  24 = 9 eggs with cracks.

Therefore the number of eggs without cracks can be calculated by the subtraction of total eggs from the eggs with cracks.

Eggs without cracks= 72 - 9 = 63 eggs.

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Answer:

55%

Step-by-step explanation:

11/20 = x/100

cross multiply

Answer:

55%

Now we can see that our fraction is 55/100, which means that 11/20 as a percentage is 55%.

Step-by-step explanation:

In the event of describing the likelihood that the team rebounds the next missed shot is likely, and the number of rebounds that the team should expect to have missed in 15  shots is 10.5 rebounds.

Given

Number of shots missed by the given team is 7

Total number of shots fired is 10

a) Then, moving on to the first part of the question

Here we have to apply probability to evaluate the likelihood of the given team rebounds the next missed shot.

Then,

Probability = no of shots attended / total number of shots fired

Probability = 7 /10

Then the event is likely

b) Now the second part

Then the number of rebounds the given team expect to have in the next 15 missed shots

= 7/10 ×15

= 105/10

= 10.5 rebounds

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By mathematical induction, we can conclude that the sum of any four consecutive integers has the form 4k+2 for some integer k.

To prove that the sum of any four consecutive integers has the form 4k+2 for some integer k, we can use mathematical induction.

Let's start with the base case: four consecutive integers starting from 1 are 1, 2, 3, and 4. Their sum is 10, which can be written as 4(2)+2. So the statement holds true for the base case.

Now let's assume that the statement is true for some arbitrary set of four consecutive integers a, a+1, a+2, and a+3. We want to show that it also holds true for the next set of four consecutive integers: a+1, a+2, a+3, and a+4.

The sum of these four consecutive integers is (a+1) + (a+2) + (a+3) + (a+4) = 4a + 10. We can rewrite this as 4(a+2) + 2, which is in the form 4k+2, where k is equal to (a+2).

Therefore, we can conclude that the sum of any four consecutive integers has the form 4k+2 for some integer k.

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Jada can take the piece with the crust, and Andre can take the piece without the crust. This way, they will each have an equal portion of the pizza slice, and Andre won't have to eat any crust.

To divide the pizza slice into two equal pieces so that Andre doesn't have to eat any crust, Jada and Andre can follow the following steps;

Firstly, find the area of the pizza slice

The area of the sector of a circle is given by the formula A = (1/2) × r² × θ, where r is radius of the circle and θ is the central angle in radians. In this case, the radius of the pizza slice is 20 cm and the central angle is π/3 radians. Plugging in these values, we can calculate the area of the pizza slice.

A = (1/2) × (20 cm)² × (π/3)

A = (1/2) × 400 cm² × (π/3)

A = 200/3 × π cm²

Now, find half of the area of the pizza slice.

To divide the pizza slice into two equal pieces, Jada and Andre need to find half of the total area of the pizza slice.

Half of the area of the pizza slice = (1/2) × (200/3 × π cm²)

Half of the area of the pizza slice = 100/3 × π cm²

However,  Cut along the radius.

Jada and Andre can cut along the radius of the pizza slice, starting from the center of the circle (where the crust is) and extending to the outer edge of the pizza. This will result in two equal pieces, with one piece containing the crust and the other piece not containing any crust.

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Answer:

23,040 students

Step-by-step explanation:

The football field is 360 feet long and 160 feet wide. To calculate the area, we multiply those 2 numbers:

360 * 160 = 57,600²

Now considering that the expected floor space a person occupies is 2.5 sq feet, we divide 57,600 by 2.5:

57,600/2.5 = 23,040

So 23,040 students can fit on the football field.

1) The length, width, and height of the box are 11 cm, 11 cm, and 11 cm respectively.

2) The shape of the cross section when the box is cut parallel to the base is a square.

3) The surface area of the box is 726 cm².

4) The surface area of the box if it is scaled up by a factor of 10 is 7260 cm².

5) The volume of the box is 1331 cm³.

6) The volume of the box if it is scaled down by a factor of 133. 1 cm³ is 10 cm³.

What is the cuboid shape?

A cuboid is a hexahedron, or a solid with six faces, in geometry. Quadrilaterals make up its faces. Cuboid implies "like a cube," in the sense that a cuboid can be converted into a cube by varying the length of its edges or the angles between its faces.

Given that the dimension of a box is 11 cm x 11 cm x 11 cm.

1) The dimension of a box can be written as length x width x height.

The length, width, and height of the box are 11 cm, 11 cm, and 11 cm respectively.

2) The length and width of the base of the box is 11 cm and 11 cm respectively. Since the length and width of the base same thus the base is a square.

The shape of the cross-section when the box is cut parallel to the base is the same as the base. The shape is a square.

3) The surface area of the cubic is 6 x area of the base

= 6 x 11 x 11

= 726 cm²

4) The surface area of the box if it is scaled up by a factor of 10 is

= 726 cm² x 10

= 7260 cm²

5) The volume of a cube is length x width x height

The volume is 11 cm x 11 cm x 11 cm = 1331 cm³

6) The volume of the box if it is scaled down by a factor of 133. 1 cm³  is

= 1331/ 133. 1 cm³

= 10 cm³

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Answer:

Step-by-step explanation:

are the what???

Answer:

Fraction form: 1/2

Decimal Form: 0.5

Step-by-step explanation:

2 x  1/2 x 1/2

Keep in mind each time you are trying to find the Volume of a Prism make sure to multiply the length x width x height.

Answer:

The equation of the graph is;

y = 4·x

Step-by-step explanation:

The coordinates of two points, (x₁, y₁), and (x₂, y₂) respectively on the straight line graph are;

(-3, 12), and (2, 8)

The slope, m, of the straight line graph is given as follows;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Therefore, by substitution of the values, we have;

\(Slope, \, m =\dfrac{8-(-12)}{2-(-3)} = \dfrac{8 + 12}{2 + 3} =\dfrac{20}{5} = 4\)

The equation of the graph in point slope form is therefore;

(y - 8) = 4×(x - 2)

y = 4·x - 8 + 8 = 4·x

y = 4·x.

Answer:

118.0

Step-by-step explanation:

using Trigonometry,

\(x = 99tan(50) \\ = 118.0\)

Answer:

A: y = -4/5x + 3/2 i believe is the correct answer

Step-by-step explanation:

(a) To determine if {{A,D,E},{B,C},{D,F}} is a partition of set K={A,B,C,D,E,F}, we need to check two conditions:

1. Each element of K should be in exactly one subset of the partition.

2. The subsets of the partition should be disjoint.

Let's examine the subsets of the given partition:

Subset 1: {A, D, E}

Subset 2: {B, C}

Subset 3: {D, F}

Condition 1 is satisfied because each element of K appears in one and only one subset. All elements A, B, C, D, E, and F are covered.

Condition 2 is not satisfied because Subset 1 and Subset 3 have an element in common, which is D. Subsets in a partition should be disjoint, meaning they should not share any elements.

Therefore, {{A,D,E},{B,C},{D,F}} is not a partition of set K.

(b) To determine if {{3,7,8},{2,9},{1,4,5}} is a partition of set L={1,2,3,4,5,6,7,8,9}, we again need to check the two conditions for a partition.

Let's examine the subsets of the given partition:

Subset 1: {3, 7, 8}

Subset 2: {2, 9}

Subset 3: {1, 4, 5}

Condition 1 is satisfied because each element of L appears in one and only one subset. All elements 1, 2, 3, 4, 5, 6, 7, 8, and 9 are covered.

Condition 2 is satisfied because the subsets are disjoint. There are no common elements among the subsets.

Therefore, {{3,7,8},{2,9},{1,4,5}} is a partition of set L.

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Answer:

42: 1,2,3,6,7,14,21,and 42

GCF of 42 & 15: 3

GCF of 42 & 50: 2

Step-by-step explanation:

have a day

Answer:

3 and 2

Step-by-step explanation:

The factors of 42 are 1,2,3,6,7,14,21,42;

The factors of 15 are 1,3,5,15.

The factors of 42 are 1,2,3,6,7,14,21,42;

The factors of 50 are 1,2,5,10,25,50

The area of the region is (3/4)ab.

Given: Let A and B be points in the plane. The region S is defined in the first quadrant consisting of those points such that ∆ABC is an acute triangle.

In a coordinate plane, let A be (0,a) and B be (b,0).

Let C be a point (x,y) in the first quadrant so that the ∆ABC is acute.

Then the slope of AB is  -a/b and the slope of AC is y/x.

The angle ∠BAC is acute if and only if -a/b . y/x < -1, i.e. ab > xy.

Since we want the region in the first quadrant consisting of those points such that ∆ABC is an acute triangle, we need to graph the set of all points in the first quadrant that satisfy the inequality ab > xy.

Area of the region S = area of first quadrant - area of shaded region

Area of first quadrant = a * b

Area of shaded region = (1/2) * b * a/2 = ba/4

Thus, the area of the region S is given by a*b - ba/4 = (3/4)ab

Therefore, the area of the region is (3/4)ab.

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Fraction is a quantity representing part of a hole. The specified fraction's quotient is obtained as: Option A: -343

If we have \(a^b\), then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).

Exponentiation(the process of raising some number to some power) have some basic rules as:

\(a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\ a^b \times a^c = a^{b+c}\)

For given case, the quotient of fraction is obtained as:

\(\dfrac{(-7)^2}{(-7)^{-1}} = (-7)^2 \times (-7)^{-(-1)} = (-7)^{(2 + 1)} = -7^3 = -343\)

Thus, The specified fraction's quotient is obtained as: Option A: -343

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Answer:

a if u don't want to read lma o

Step-by-step explanation:

Answer:

it's the one on the bottom right of the screen

The total cost of repayment over 5 years is $23,300.

A loan repayment refers to the act of paying back money previously borrowed from a lender.

To get total cost of repayment, we must principal amount, the interest rate and the duration of the loan.

The formula to get total cost of repayment is given by \(Total Cost of Repayment = Principal + Interest\)

Interest = Principal * Interest Rate * Time

Given:

Principal amount is $20,000

Interest rate is 3.3%

Duration is 5 years.

Interest = $20,000 * 0.033 * 5

Interest = $3,300

Total Cost of Repayment = Principal + Interest

= $20,000 + $3,300

= $23,300.

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Answer:30%

Step-by-step explanation:

The p-value for the given test is approximately 0.067, rounded to two significant digits. This was calculated by finding the area to the right of z=1.5 under the standard normal distribution.

It is given that Null hypothesis: H0: μ ≤ 0, Alternative hypothesis: H1: μ > 0, Population standard deviation: σ = 1, Test statistic: z = 1.5

To find the p-value, we need to calculate the probability of observing a z-value of 1.5 or greater under the null hypothesis. Since the population follows the standard normal distribution, we can use a standard normal table or a calculator to find this probability.

Using calculator, we can find that the area to the right of z = 1.5 is approximately 0.0668 (rounded to four decimal places).

Since this is a one-tailed test with the alternative hypothesis in the right tail, the p-value is equal to the area in the right tail beyond the observed z-value. Therefore, the p-value for the test is approximately 0.067 (rounded to two significant digits).

So, the p-value for the given test is 0.067 (rounded to two significant digits).

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Discrete mathematics is focused on discrete objects and the relationships between them, while calculus is focused on continuous change and motion.

Discrete mathematics and calculus are two branches of mathematics that deal with different types of mathematical objects and concepts. Discrete mathematics studies discrete objects, such as integers, graphs, and algorithms, while calculus deals with continuous and smooth objects and their derivatives and integrals.

Discrete mathematics provides the mathematical foundations for computer science, especially in areas such as algorithm design, data structures, and complexity theory.

In contrast, calculus is a branch of mathematics that focuses on continuous change, and provides a foundation for many other branches of mathematics and science, including physics, engineering, and economics.

In discrete mathematics, concepts are studied in a finite and countable manner, meaning that the objects and structures being studied can be counted and identified.

For example, in graph theory, discrete mathematical structures like vertices and edges are studied and their properties are analyzed. In discrete mathematics, the focus is on finding relationships between discrete objects and how they can be manipulated, such as in combinatorics and number theory.

On the other hand, calculus deals with the study of change and motion, specifically the rate at which objects change and the accumulation of these changes over time.

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Answer:

d=5√2 unit

Step-by-step explanation:

distance between two points d=√(x2-x1)²+(y2-y1)²

two pints (-3,-4) and (4,-5)

d=√(4-(-3)²+(-5-(-4)²

d=√(4+3)²+(-5+4)²

d=√49+1

d=√50

d=√25*2

d=5√2

Answer

\( \boxed{5 \sqrt{2} \: \: \:units}\)

Step by step explanation

Let the points be A and B

A ( - 3 , - 4 ) ⇒( x₁ , y₁ )

B ( 4 , - 5 )⇒( x₂ , y₂ )

Now, let's find the distance between these points :

Distance = \( \mathsf{ \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }\)

Plug the values

⇒\( \mathsf{ \sqrt{ {(4 - ( - 3))}^{2} + {( - 5 - ( - 4))}^{2} } }\)

Calculate

⇒\( \mathsf{ \sqrt{ {(4 + 3)}^{2} + {( - 5 + 4)}^{2} } }\)

⇒\( \mathsf{ \sqrt{ {(7)}^{2} + {( - 1)}^{2} } }\)

Evaluate the power

⇒\( \mathsf{ \sqrt{49 + 1} }\)

Add the numbers

⇒\( \mathsf{ \sqrt{50} }\)

Simplify the radical expression

⇒\( \mathsf{5 \sqrt{2} \: \: units}\)

Hope I helped!

Best regards!!

Answer:

1

Step-by-step explanation:

3.2/0.4=8

8×2=16

16×0.4=6.4

6.4÷0.1=64