Solve this system of equations by subsitution {y= 2x +3
3x + 2y = 12

We discover that only the equation associated with answer option D meets all four criteria and has the right vertex:

[tex]y = -2(x - 2)^2 - 6[/tex]

The supplied coordinates (-1, 7), (0, 0), (4, 0), and are all on the graph of this equation, which has a vertex at (2, -6) (5, 7). Hence, D is the right response.

The equation is a mathematical and physical statement that defines physical occurrences. It usually consists of a variable that only presents a physical quantity, with a possible personal variable such as your energy being pointed out.

The function y = x2 - 6 provides the answer to this equation. The vertex of the parabola is (2, -6), which may be determined by calculating the equation's derivative and setting it to 0. The graph includes the coordinates (- 1, 7), (0, 0), (4, 0), and (5, 7) because they are the answers to the equation.

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The required measures of the angles are the following: ∠J = 135°, ∠F = 45°, ∠B = 135°, and ∠C = 22°.

The supplementary angles are illustrated as when pairing of angles addendum to 180° then they are called supplementary angles.

The measure of the angles are given as follows:

∠I = 22°

∠A = 23°

∠J = 180° - ∠I - ∠A (sum of interior angles in a triangle)

∠J = 180° - 22° - 23° = 135°

∠F = 180° - ∠J (supplementary angles)

∠F = 180° - 135° = 45°

∠B = 360° - 90° - 90° - 45° (sum of interior angles in the quadrilateral)

∠B = 135°

∠C = 180° - ∠A - ∠B (sum of interior angles in a triangle)

∠C = 180° - 23° - 135° = 22°

Thus, the required measures of the angles are the following: ∠J = 135°, ∠F = 45°, ∠B = 135°, and ∠C = 22°.

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Answer:

36 green marbles

Step-by-step explanation:

If 60% of the 60 marbles in the bag are green, then the number of green marbles can be calculated as:

Green marbles = 60% x 60 marbles

To simplify this calculation, we can convert 60% to a decimal by dividing by 100:

Green marbles = 0.60 x 60 marbles

Green marbles = 36 marbles

Therefore, Rudy received 36 green marbles.

Answer: 36

Step-by-step explanation:

60 is 6/10 of 100 so if you are taking a percent of 60 just multiply the percentage by 6/10. 6/10 of 60 is 36

According to the information, we can infer that the equation expressed by the parable symmetry axis is x = −b2a.

The symmetry axis of a parable is a term that refers to a vertical line that divides the parable into two congruent halves. The axis of symmetry always passes through the vertex of the parable.

To find the symmetry axis of this parable we must perform the following procedure taking into account the following information:

Additionally, we must compare the equation with y = ax2+bx+c to find the values of a, b, and c. Then these values would be like this:

According to the above, we can replace these values to solve the equation of axis of symmetry. then, the graph of a quadratic equation in the form Y = Ax2+Bx+C has ss its axis of symmetry the line X = −B2a.

Note: This Question is incomplete. Here is the complete information:

Attached Image

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The conditions which will construct a triangle as required to be identified are;

The triangle inequality theorem suggests that the sum of any two side lengths of a triangle must be greater than the third side and the difference of any two side lengths must be less than the third side.

Also, the sum of interior angles of a triangle is; 180°.

Hence, the conditions as required are; Angles 20°, 150°, 10° and Side lengths 11 cm, 4 cm, 8 cm.

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The period of the sine function is given as follows:

2π.

Hence the frequency is given as follows:

0.5/π Hz.

The standard definition of a sine function is given as follows:

y = Asin(Bx + C) + D.

The parameters are given as follows:

A: amplitude.

B: the period is 2π/B.

C: phase shift.

D: vertical shift.

From the function defined in this problem, the parameter B is given as follows:

B = 1.

Hence the period of the function is given as follows:

P = 2π/1 = 2π.

The frequency is the inverse of the period, hence it is given as follows:

f = 1/p

F = 1/(2π)

F = 0.5/π Hz.

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After constructing the scatter-plot chart, we can find that the Final and Mid-term have a negative relationship.

Dots are used in a scatter plot, also known as a scatter chart or scatter graph, to represent the values of two different numerical variables. The values of a data point are represented by the position of each dot on the horizontal and vertical axes. To view relationships between variables, utilize scatter plots. Scatter plots are primarily used to evaluate and present correlations between two numerical variables. When the data are viewed as a whole, the patterns shown by the dots in a scatter plot are in addition to the values of the individual data points.

Now in the given question, after drawing the scatter chart we can see a strong downward slope which represents a negative linear relationship.

Therefore, the Final and Mid-term have a negative relationship.

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The complete question is:

The accompanying table shows a portion of mid-term and final grades for 32 students.

Construct a scatterplot of Final against Mid-term. Given the scatterplot, which statement best describes the relationship between the Final and Mid-term?

A. Final and Mid-term have a negative relationship.

B. Final and Mid-term have a positive relationship.

C. Final and Mid-term have no relationship.

D. Final and Mid-term have a U-shaped (nonlinear) relationship.

Check the picture below.

The smallest number in our sample of 11 numbers that is greater than or equal to 40% of the numbers.

In arithmetic, a percentage is a ratio or ratio that is presented as a part of 100. Usually, the acronyms "pct.," "pct," and "pc" are also utilized. Yet it is broadly classified into the following by the percent sign, "%." The % sum has no dimensions. Rates are essentially fractions when the sum is 100. Use the percent sign (%) to indicate that a number seems to be a percentage by placing it next to it. For illustrate, you score a 75% if you properly answer 75 out of 100 respondents on a test (75/100). Divide the money by total and multiply it by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.

given

The 40th percentile's ordinal rank is equal to (40/100) X 10 (or 4).

50 is the 40th percentile and the following rank is 5 with 50 as the data value.

We observe that 50 is greater than 10, 20, 30, or 40% of the data,

4/10 = 0.4.

The smallest number in our sample of 11 numbers that is greater than or equal to 40% of the numbers.

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The probability mass function for the random variable would be 0.38742049.

In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value.

Probability mass function is the probability distribution of a discrete random variable, and provides the possible values and their associated probabilities. It is the function [tex]{\displaystyle p:\mathbb {R} \to [0,1]}[/tex] defined by -

[tex]${\displaystyle p_{X}(x)=P(X=x)}[/tex].

Given is that the probability of corrosion is 0.1 under specific values of half-cell potential and concrete resistivity. the risk of corrosion in five independent grids of a building with these values of half-cell potential and concrete resistivity is investigated now.

We can write the

[tex]$f(x;n,p) = \frac{n!}{x!(n-x)!}\; p^{x} \;(1-p)^{n-x}[/tex]

where -

{x} = number of successes

{n} = number of trials

{p} = probability of a successful outcome

Substituting the values, we get -

[tex]$f(1;10,0.1) = \frac{10!}{1!(10-1)!}\; (0.1)^{x} \;(1-0.1)^{10-1}[/tex]

[tex]$f(1;10,0.1) = 0.38742049[/tex]

Therefore, the probability mass function for the random variable would be 0.38742049.

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When a cube's top is chopped off to create a rectangular box, the original cube's side length is 5.43 feet as a result.

A rectangular is a square with four right angles in Euclidean geometry and trigonometry. You may also speak to it as an equiangular tetra, meaning that all of its edges are equal. A straight angle could also be found in the parallelogram. Rectangles with four evenly sized sides are called squares. Four 90 ° vertices and equal equal sides make up a quadrant with the look of a rectangle. As a basis, it's also known as a raster images rectangle. A rectangle is also referred to as a trapezoidal since its opposite angles are equal but parallel.

given

Let x represent the cube's edge in feet.

Cube volume equals side 3

Hence, the given cube's volume,

The top of a cube is now chopped off in a 4 foot thick chunk.

The slice's volume is equal to x x x 4 = 4x2 ft2.

The volume of the final figure is therefore equal to the sum of the volumes of the cut and cube figures.

= ( x³ - 4x² ) ft²

The answer to the query is

Finding the zeros of the function will lead to the discovery of the solution to the aforementioned equation ( by graphing ),

We discovered that

The equation's graph crosses x at (5.426,0)

Hence, 5.426 is the equation's zero.

⇒ x = 5.426 ≈ 5.43

When a cube's top is chopped off to create a rectangular box, the original cube's side length is 5.43 feet as a result.

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the variance will be 0.6217.

What is frequency distribution?

The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.

A small data analysis class has six computer science majors among the fourteen total students.

Three people are chosen at random to form a group.

here this is hypergeometric distribution with parameter n=sample size =3 ; N =population size =14

and k=computer sience major =6

a) E(X) =nk/N =3*6/14 =18/14 =9/7 =1.2857

b)|varaince =σ²=(nk/N)*(1-k/N)*(N-n)/(N-1)) =(3*6/14)(1-6/14)*(14-3)/(14-1)= 0.6217

Hence, the variance will be 0.6217.

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the equation "y = 2x + 7" represents a proportional relationship.

Refer to the image attached.

Answer:

48.

Step-by-step explanation:

Area of a rectangle formula is [tex]l[/tex]·[tex]w[/tex]

[tex]6[/tex] · [tex]8[/tex] [tex]= 48[/tex]

Thus, the area of the rectangle equals 48.

200 pounds need to collect to earn the $50.00. Divide the cost per pound from the total amount needed, [tex]\frac{50.00}{0.25}[/tex]= 200 pounds.

The official money of the U.k. and its regions is the GBP, or British pound sterling. The Pound is the earliest currency that is still accepted as legal tender in the entire world. The GBP, represented by pound sign (£), has one of the greatest trade volumes worldwide.

The development of the pounds sterling -The Latin word "libra," which means balance and weight, is where the name "pound sterling" comes from. During the years, the pound banknotes underwent various revisions before being initially printed by the Bank of England and over 300 years ago.

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Answer:

A. 25% off $20

C. $14 plus 7% sales tax

D. $14 plus 7% sales tax

E. 20% off $18 then a 10% shipping fee

Step-by-step explanation:

The rest i did the math and it doesnt add up. But your option B. is either typoed or i dont know. If its a typo then include that in your answer as well

Answer:

D) -53.23

Step-by-step explanation:

Use PEMDAS to evaluate the expression

We do parentheses first.

[tex]|65.45-42.45|-76.23[/tex]

Evaluate what's inside of the absolute value bracket.

[tex]|23|-76.23[/tex]

Simplify

[tex]23+-76.23[/tex]

Evaluate

-53.23

The expression b²c²d³f⁴ - 4dfbc² when simplified is bdc²f(bd²f³ - 4)

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

b²c 2d³f4 - 4d fl b[ ]c[] -2​

Express properly

So, we have the following representation

b²c²d³f⁴ - 4dfbc²

Factor out dc² from the expression

So, we have the following representation

b²c²d³f⁴ - 4dfbc² = dc²(b²d²f⁴ - 4fb)

Factor out f from the expression

So, we have the following representation

b²c²d³f⁴ - 4dfbc² = dc²f(b²d²f³ - 4b)

Factor out b from the expression

So, we have the following representation

b²c²d³f⁴ - 4dfbc² = bdc²f(bd²f³ - 4)

Hence, the expression is bdc²f(bd²f³ - 4)

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The amount of cards in each row is a factor of 60 in each scenario, ensuring that Vildia will utilize all 60 cards and that there will be an equal number of cards in each row.

In mathematics, a combination is a way of selecting a subset of items from a larger set, where the order of the selected items does not matter. A combination is different from a permutation, which is a way of selecting a subset of items from a larger set, where the order of the selected items does matter.

Here,

If Vildia wants to set up a card game using 60 cards and wants to make an array with the same number of cards in each row, she could arrange the cards in the following ways:

1 x 60: In this case, Vildia would arrange all 60 cards in a single row.

2 x 30: In this case, Vildia would arrange the cards in two rows, each containing 30 cards.

3 x 20: In this case, Vildia would arrange the cards in three rows, each containing 20 cards.

4 x 15: In this case, Vildia would arrange the cards in four rows, each containing 15 cards.

5 x 12: In this case, Vildia would arrange the cards in five rows, each containing 12 cards.

6 x 10: In this case, Vildia would arrange the cards in six rows, each containing 10 cards.

10 x 6: In this case, Vildia would arrange the cards in ten rows, each containing 6 cards.

12 x 5: In this case, Vildia would arrange the cards in twelve rows, each containing 5 cards.

15 x 4: In this case, Vildia would arrange the cards in fifteen rows, each containing 4 cards.

20 x 3: In this case, Vildia would arrange the cards in twenty rows, each containing 3 cards.

30 x 2: In this case, Vildia would arrange the cards in thirty rows, each containing 2 cards.

60 x 1: In this case, Vildia would arrange all 60 cards in a single column.

Note that in each case, the number of cards in each row is a factor of 60, which ensures that Vildia will use all 60 cards and that there will be an equal number of cards in each row.

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The answers to the probability problem have been stated below

The mean of the distribution would be 29

The standard deviation would be  8.7/√40 = 1.38

If the sample was larger, the mean would stay the same, the standard error would decrease.

3. The corresponding z score with

43.8 - 29 / 8.7

= 1.70

b. z = (43.8-29)/(8.7/√40) = 8.94

14.8 /1.38

= 10.7

c) the fisherman is more likely to catch one fish

d) z = (30.8-29)/(8.7/√40) = 1.26

= 1.8 / 1.38

= 1.304

e) He is more likely to catch 40 fishes.

4.a) Proportion in the middle = 0.95

Proportion on left and right side of normal curve = (1-0.95)/2

= 0.025

Z score at p = 0.025 using excel = NORM.S.INV(0.025) = 1.96

X1 = µ - z*σ = 29 - (1.96)*8.7

= 11.948

X2 = µ + z*σ = 29 + (1.96)*8.7

= 46.052

between 11.948 and 46.052

b)

Proportion in the middle = 0.95

Proportion on left and right side of normal curve = (1-0.95)/2 = 0.025

NORM.S.INV(0.025) = 1.96

x1 =  29 - (1.96)*8.7/√40

= 29 - 2.698

= 26.30

x2 = 29 + 2.698

= 31.698

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Answer:Mike has $100. He wants to buy a bike that costs $75 and three speakers that cost $30 each. trade of is example of Opportunity cost

Step-by-step explanation:

Answer:

Please Mark As Brainliest Answer

Step-by-step explanation:

In many contexts, we can estimate distances between objects or locations, but we may not always be able to measure them precisely. There are several reasons why we might only be able to estimate distances rather than measure them exactly:

Limitations of measuring instruments: The precision of a measuring instrument can limit our ability to measure distances accurately. For example, a ruler may only have markings up to a certain level of precision, so we may need to estimate distances between the markings.

The variability of the distance: In some cases, the distance we are measuring may be constantly changing, making it difficult to measure with precision. For example, if we are trying to measure the distance between two moving objects, the distance between them will constantly change, and we may need to estimate the distance at a particular moment in time.

Environmental factors: The environment can also make it difficult to measure distances precisely. For example, atmospheric conditions such as haze or fog can obscure objects and make it difficult to judge their distance accurately.

Human perception and judgment: Finally, our own perception and judgment can also limit our ability to measure distances accurately. For example, when estimating the distance to an object, our perception of the size of the object can affect our judgment of its distance.

In many cases, despite these limitations, estimates of distances can still be useful and informative. For example, in navigation, we may not need to know the exact distance between two points, but only an estimate that is accurate enough to help us navigate from one point to the other

Answered By Unish ©

Verified Answer ✅

Answer: 1/64 cubic inch

Step-by-step explanation:

Side of cube = 1/4

Volume = s^3 = 1/4^3

= 1/64

Hope this helps!!

The sample space for x, where x is the number of shots the basketball player makes out of 5 free throws, is,{SSSSS, FSSSS, SFSSS, SSFSS, SSSF S, SSSSF, FSSF S, FSFSS, FSSSF, SFFSS, SFSSF, SSFFS, FSSFS, FSFSS, FFSSS, SFFSF, SFSSF, SSFSF, FSSSF, FSFSS, SFSFS, FSSFS, FSSSF, SFFFS, SSFFS, FFSFS, FFSFF, FSFFS, SFSFF, SFSSS}There are 32 possible outcomes in the sample space.

The sample space for x is the set of all possible outcomes of the experiment of shooting 5 free throws. Since each shot can either be made or missed, there are 2 possible outcomes for each shot. Therefore, there are 2^5 = 32 possible outcomes for the experiment.

To enumerate the sample space, we can use the notation S for made shots and F for missed shots. Then, each outcome of the experiment can be represented by a string of 5 letters, where each letter represents the outcome of a single shot.

Using this notation, the sample space for x is:

{SSSSS, FSSSS, SFSSS, SSFSS, SSSF S, SSSSF, FSSF S, FSFSS, FSSSF, SFFSS, SFSSF, SSFFS, FSSFS, FSFSS, FFSSS, SFFSF, SFSSF, SSFSF, FSSSF, FSFSS, SFSFS, FSSFS, FSSSF, SFFFS, SSFFS, FFSFS, FFSFF, FSFFS, SFSFF, SFSSS}

Note that there are 6 outcomes where the player makes 0 shots, 5 outcomes where the player makes 1 shot, 10 outcomes where the player makes 2 shots, 10 outcomes where the player makes 3 shots, 5 outcomes where the player makes 4 shots, and 1 outcome where the player makes all 5 shots.

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Using exponent rules we can simplify the expression to get:

√y³⁶ =  y¹⁸

Here we want to simplify the expression below:

√y³⁶

Remember that the square root is equivalent to an exponent of 1/2, then we can rewrite:

√y³⁶ = (y³⁶)¹´²

And that will be equal to:

(y³⁶)¹´² = y³⁶´² = y¹⁸

That is the expression simplified.

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The height of the given triangle having an area of 13.5in.² and a base length of 6.75 in. is 4 in.

What is a triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. Any three points in Euclidean geometry, when they are not collinear, produce a distinct triangle.

In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.

In this question, we are given,

Area of triangle A = 13.5 in.²

Base of triangle b = 6.75 in.

We are asked to find the height h of the triangle.

Now formula of the area is:

A = 1/2 * b * h

13.5 = 1/2 * 6.75 * h

h = 13.5 *2 / 6.75 = 4 in.

Therefore the height of the given triangle is 4 in.

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The point slope form of a linear equation is an equation that describes the relationship between two variables, x and y, in terms of their linear relationship.

It takes the form:.y - y₁ = m(x - x₁)

where (x₁, y₁) is a point on the line and m is the slope of the line.

In this form, you can find the equation of a line if you know a point on the line and the slope of the line. You can also use this form to find the equation of a line if you are given two points on the line, by first finding the slope using the two points, and then plugging in one of the points and the slope into the equation.

The point slope form can be useful in a variety of contexts, such as in graphing and in solving problems involving rates of change.

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