Choose the value of x that makes the open sentence true.
40−x²<2x+15

a. 2
b. 3
c. 4
d. 5

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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Liam needs to make at least 9 visits to earn his first free movie ticket.

A mathematical statement expressing a connection between two values or expressions that aren't always equal is called an inequality. It makes reference to the connection between the two values using one of the inequality symbols. Algebra, calculus, optimization, as well as practical applications in the domains of economics, physics, and engineering, all frequently involve inequality concepts. They are also employed in daily life to convey restrictions or limitations, such as when establishing budgets or making choices depending on the availability of resources.

Let us suppose the number of visits = x.

Given that, He receives 50 rewards points just for signing up. He earns 12.5 points for each visit to the movie theater.

Thus,

50 + 12.5x ≥ 160

12.5x ≥ 110

x ≥ 8.8

Rounding to the nearest whole number:

x ≥ 9

Hence, Liam needs to make at least 9 visits to earn his first free movie ticket.

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Answer:

5/3 = 1.6666666667

or 1.7 rounded to the nearest tenth

Answer:

Since p-value > ∝, H0 is accepted

Step-by-step explanation:

Calculating gives the following results.

ANOVA Table

Source DF               Sum             Mean      F Statistic P-value

                                 of Square           Square

Groups     6         191.61                      31.935        0.020          0.999

(b/w groups)

Error

(within 14          21736.08                1552.577

groups)                                                                                                    

Total  20          21927.69 1096.385                                          

1. H0 hypothesis

Since p-value > ∝, H0 is accepted.

Hence the averages of all groups considered to be equal.

Or the difference between the averages of all groups is not big enough to reject H0.

2. P-value

P-value equals 0.999. This means that if we would reject H0, the chance of type1 error (rejecting a correct H0) would be too high i.e  (99.99%)

The bigger  p-value  supports H0.

3. The statistics

The test statistic F equals 0.020, which lies in the accepted range: [-∞ : 2.8477]

The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Total of 22 is more than 4500 is equivalent to average of 22 is more than \($\frac{4500}{22}\)=204.545

\($$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$\)

                        = 1 - 0.8997

                        = 0.1003

                        = 10.03%

Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

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Answer:

50 + 25 = 75

50 - 25 = 25

The numbers are 50 and 25

Step-by-step explanation:

The sum of two numbers is 25 and their difference is 75. What are the two numbers? Let's start by calling the two numbers we are looking for x and y.

The sum of x and y is 25. In other words, x plus y equals 25 and can be written as equation A:  

x + y = 75

The difference between x and y is 75. In other words, x minus y equals 75 and can be written as equation B:

x - y = 75

Now solve equation B for x to get the revised equation B:  

x - y = 25

x = 25 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 75

25 + y + y = 75

25 + 2y = 75

2y = 50

y = 25

Now we know y is 25. Which means that we can substitute y for 25 in equation A and solve for x:

x + y = 75

x + 25 = 75

X = 50

Therefore,

Sum: 50 + 25 = 75

Difference: 50 - 25 = 25

Hope this helps! :D

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{MN}\\ o=\stackrel{opposite}{18} \end{cases} \\\\\\ MN=\sqrt{ 30^2 - 18^2} \implies MN=\sqrt{ 576 }\implies MN=24 \\\\[-0.35em] ~\dotfill\\\\ \cos(M )=\cfrac{\stackrel{adjacent}{24}}{\underset{hypotenuse}{30}} \implies \cos(M)=\cfrac{4}{5}\)

To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

A.y-intercept: 4

axis of symmetry: x=2

x-coordinate of the vertex: 2

B.x f(x)

  0   4

  1   1

  2   0

  3     1

  4   4

C. 5 |           .  

      |        .    

      |     .        

      |  .            

      |.                

  0 |_____________

      0  1  2  3  4

An intercept refers to the point(s) at which a curve or line intersects an axis. For example, the x-intercept is where the line crosses the x-axis, and the y-intercept is where it crosses the y-axis.

A vertex is a point where two or more lines or curves meet. In the context of a parabolic curve, the vertex is the point at which the curve changes direction.

According to the given information:

A. The y-intercept occurs when x=0. Therefore, f(0) = 0² - 4(0) + 4 = 4. So the y-intercept is (0, 4).

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are the coefficients of x² and x, respectively. In this case, a = 1 and b = -4, so x = -(-4)/(2*1) = 2. Therefore, the equation of the axis of symmetry is x = 2.

To find the vertex, we use the fact that the vertex occurs at the axis of symmetry. So when x=2, f(x) = 2² - 4(2) + 4 = -4. Therefore, the vertex is at (2, -4).

B. We can use the vertex to make a table of values:

x f(x)

0 4

1 1

2 0

3 1

4 4

C. We can use the table of values to plot the points and sketch the graph of the function. The graph of the function is a parabola that opens upward, since the coefficient of x² is positive.

  5 |           .  

      |        .    

      |     .        

      |  .            

      |.                

  0 |_____________

      0  1  2  3  4

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Answer:

9 x 1/12 = 4 1/2

Answer:

43.96 or C

Step-by-step explanation:

c=(pi)(d)

pi --> 3.14

d --> diameter (in your case 14.)

c=3.14*14

c= 43.96

Both formulas work, 2(pi)r and (pi)(d)

But, if they give you the diameter then use (pi)(d).

If they give you the radius then use 2(pi)r

Answer:

13/18

Step-by-step explanation:

4/8 simplyfies to 1/2. 1/2 + 2/9= 9/18 +4/18= 13/18

Answer:

Step-by-step explanation:

From the given information:

x                     y                     xy                   x²                        y²

4                     4                     16                  16                        16

12                   10                   120                 144                     100

14                   13                   182                  196                     169

20                 15                   300                 400                    225

23                 15                   345                  529                    225

30                 25                 750                   900                    625

40                 27                 1080                 1600                    729

48                 44                 2112                  2304                  1936

55                 38                 2090               3025                   1444

67                 46                 3082               4489                    2116

72                 53                 3816                 5184                  2809

85                 71                 6035                 7225                  5041

96                 82               7872                 9216                   6724

112                 99               11088                12544                 9801

127                 101              12827                16129                10201

\(\sum _{xi} = 805\)      \(\sum_{yi} = 643\)    \(\sum_{x_iy_I}= 51715\)   \(\sum_{x_i^2}= 63901\)    \(\sum_{y_i^2} = 42161\)

The least-square regression equation is: \(\hat y = b_o+b_1 x\)

\(b_1 = \dfrac{n \sum xy - ( \sum _x) ( \sum_y)}{n \sum x^2 - ( \sum x)^2}\)

\(b_1 = \dfrac{15(51715) - (803) (643)}{15(63901)-(805)^2}\)

\(b_1 = \dfrac{775725-516329}{958515-648025}\)

\(b_1 = \dfrac{259396}{310490}\)

b₁ = 0.835440

∴ Slope term, b₁ = 0.835

\(SS_{XX} = \sum x^2 - \dfrac{(\sum x)^2}{n}= 63901 - \dfrac{(805)^2}{15}=20699.33\)

\(SS_{yy} = \sum y^2 - \dfrac{(\sum y)^2}{n }= 42161 - \dfrac{(643)^2}{15}= 14597.73\)

\(SS_{xy} = \sum xy - \dfrac{(\sum x) (\sum y)}{n}= 51715 - \dfrac{(803)(643)}{15}= 17293.067\)

\(SST = SS_{yy}= 14597.73\)

\(SSR = \dfrac{SS_{xy}^2}{SS_{xx}}= \dfrac{17293.067^2}{20699.33}=14447.34\)

SSE = SST - SSR = 14597.73 - 14447.34 = 150.39

The hypothesis test for the significance of \(\beta_1\) is:

\(H_o: \beta_1 = 0 \\ \\ H_1: \beta_1 \ne 0\)

Significance level ∝ = 1 - 0.95 = 0.05

The sample slope \(b_1\) = 0.835440

\(Test \ statistic = t_{observed} = \dfrac{b_1-0}{\sqrt{\dfrac{SSE}{(n-2)SS_{xx}}}}\)

\(t_{o} = \dfrac{0.835440-0}{\sqrt{\dfrac{150.39}{(15-2)20699.33}}}\)

\(t_{o} = \dfrac{0.835440}{\sqrt{\dfrac{150.39}{269091.29}}}\)

\(t_o = 35.339\)

Degree of freedom df = n - 2

df = 15 -2

df = 13

Using the Excel formula to determine the P_value.

\(P-value = P(t, \Big|35.339 \Big|)\)

P-value = 2 × t.dist(35.339,13,1)

P-value = 0.0000

P-value = 0

Critical value: \(t_{critical} = t_{\alpha/2,df} = t_{0.05/2,13}= 2.160\)

Rejection region: To reject \(H_o\); if \(\Big | t_o \Big | > t_c\)

Decision: Since \(\Big | t_o \Big | > t_c\); we reject  \(H_o\)

Conclusion: There is enough evidence to conclude that the linear relationship between x & y

Thus; we reject \(H_o\) & there is a useful linear relationship between x & y.

The 95% C.I for slope is given by the equation:

\(=b_1 \pm t_{(\alpha/2,n-2)} \sqrt{\dfrac{SSE}{n-2}}\sqrt{\dfrac{1}{SS_{xx}} }\)

\(=0.835440 \pm 2.160 \sqrt{\dfrac{150.39}{15-2}}\sqrt{\dfrac{1}{20699.33} }\)

= 0.835440 ± 2.160 (3.40124)(0.006951)

= 0.835440 ± 0.0511

= (0.835440 - 0.0511, 0.835440 + 0.0511)

= (0.78434, 0.88654)

= (0.784, 0.887)   to three decimal places.

∴ 95% C.I of slope = \(\mathbf{( 0.784 < \beta_1 < 0.887) \ to \ 3 \ d.p}\)

Given:

Height of triangle, h = 15x - 4

Base of triangle, b = 6x

Let's find the area of the triangle.

To find the area of the triangle, apply the formula:

Where:

b = 6x

h = 15x - 4

Thus, we have:

Apply distributive property:

Therefore, the simplified algebraic exression which represents the area of the traingle is:

ANSWER:

Answer:

(5, 4)

Step-by-step explanation:

(x + 2, y + 3)

(3  + 2, 1 + 3)

(5, 4)

Answer:

B' (5, 4 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 2, y + 3 )

means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then

B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )

The sprinkler for the Cook family uses 15 liters of water per hour, whereas the Gonzalez family uses 40 liters of water per hour.

We can set up the following system of equations based on the given information:

Equation 1: x * 15 + y * 40 = 1825 (total water output equation)

Equation 2: x + y = 55 (sum of the two rates equation)

We can solve this system of equations to find the values of x and y.

Multiplying Equation 2 by 15, we get:

15x + 15y = 825

Subtracting this equation from Equation 1, we get:

25y = 1000

y = 1000 / 25

y = 40

Substituting the value of y in Equation 2, we get:

x + 40 = 55

x = 55 - 40

x = 15

Therefore, The sprinkler for the Cook family uses 15 liters of water per hour, whereas the Gonzalez family uses 40 liters of water per hour.

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Answer:

4

Step-by-step explanation:

The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = − 7 x + 4 , we see that the y-intercept of the line is 4.

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Answer:

Scientific research

Step-by-step explanation:

I don't know answer sorry mL nalang tayo

Answer:

7kg

Step-by-step explanation:

258 / 36 = 7.16

the nearest ten, 7.20

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Since a kite is a quadrilateral, it has the value of 360 total degrees.

Answer: 48843.0141

Step-by-step explanation:

Answer:

Hey mate....

Step-by-step explanation:

This is ur answer.....

763.53 x 63.97 = 48,843.0141

Or else you can refer to the image attached below, and for your more maths help you can download PHOTOMATH for free!

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Answer:

0.48 = 48% probability that an employee selected at random will need either corrective shoes or major dental work

Step-by-step explanation:

I am going to solve this question treating these events as Venn probabilities.

I am going to say that:

Event A: Employee needed corrective shoes.

Event B: Employee needed major dental work.

22% of the employees needed corrective shoes

This means that \(P(A) = 0.22\)

29% needed major dental work

This means that \(P(B) = 0.29\)

3% needed both corrective shoes and major dental work.

This means that \(P(A \cap B) = 0.03\)

What is the probability that an employee selected at random will need either corrective shoes or major dental work?

This is:

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

Replacing the values that we have:

\(P(A \cup B) = 0.22 + 0.29 - 0.03 = 0.48\)

0.48 = 48% probability that an employee selected at random will need either corrective shoes or major dental work

The equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

Let position vector of point P be:

p = 3 i + j + 2 k

Let position vector of point Q be:

q = i - 2 j - 4 k

So, PQ = Q - P

PQ = n = i - 2 j - 4 k - (3 i + j + 2 k)

n = i - 2 j - 4 k - 3 i - j - 2 k

n = - 2 i - 3 j - 6 k

The Equation of plane passing through point Q and perpendicular to PQ will be:

(r - q).n = 0

r n = q n

q n = (i - 2 j - 4 k) . (- 2 i - 3 j - 6 k)

q n = - 2 + 6 + 24

q n = 28

r n = 28

r (- 2 i - 3 j - 6 k) = 28

r (2 i + 3 j + 6 k) + 28 = 0

Therefore the equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

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Answer:

(x + 2)(x - 6)

Step-by-step explanation:

We are given the equation: x² - 4x - 12. Let's factor this.

First, look at the integer factor pairs of -12:

-1, 12

-2, 6

-3, 4

1, -12

2, -6

3, -4

We would like to find a pair whose sum is -4. Inspecting each pair, we realise that only the pair 2, -6 works because 2 + (-6) = -4.

Thus, our factors are:

x + 2    (from the 2)

x - 6     (from the -6)

The factored form of our given quadratic is:

(x + 2)(x - 6)

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Ending Inventory Cost and Cost of Goods Sold using different inventory methods:

FIFO Method:

Ending Inventory Cost: $11,920

Cost of Goods Sold: $15,068

LIFO Method:

Ending Inventory Cost: $11,996

Cost of Goods Sold: $15,123

Weighted Average Cost Method:

Ending Inventory Cost: $11,974

Cost of Goods Sold: $15,087

Using the FIFO (First-In, First-Out) method, the cost of the ending inventory is determined by assuming that the oldest units (those acquired first) are sold last. In this case, the cost of the ending inventory is calculated by taking the cost of the most recent purchases (70 units at $142 per unit) plus the cost of the remaining 10 units from the March 10 purchase.

This totals to $11,920. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory at $124 per unit, 60 units from the March 10 purchase at $132 per unit, and 20 units from the August 30 purchase at $138 per unit), which totals to $15,068.

Using the LIFO (Last-In, First-Out) method, the cost of the ending inventory is determined by assuming that the most recent units (those acquired last) are sold first. In this case, the cost of the ending inventory is calculated by taking the cost of the remaining 10 units from the December 12 purchase, which amounts to $1,420, plus the cost of the 70 units from the August 30 purchase, which amounts to $10,576.

This totals to $11,996. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,123.

Using the Weighted Average Cost method, the cost of the ending inventory is determined by calculating the weighted average cost per unit based on all the purchases. In this case, the total cost of all the purchases is $46,360, and the total number of units is 200.

Therefore, the weighted average cost per unit is $231.80. Multiplying this by the 80 units in the physical inventory at December 31 gives a total cost of $11,974 for the ending inventory. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,087.

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Because EF = GH = 4, EF≅GH, Because these are vertical line segments, their are slope undefined and they are parallel. EF and GH are opposite sides that are equal and parallel. So, EFGH is a parallelogram by the definition of a parallelogram.

What is a parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are equal in length, and its opposite angles are equal in size.

Given that E(-3,0), F(-3,4), G(3,-1),H(3,-5)

The quadrilateral is attached below.

The distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

The length of EF is √[(-3 -(-3))² + (4- 0)²] = √4² = 4

The length of GH is √[(3 -3)² + (-1- (-5))²] = √4² = 4

Therefore, EF = GH = 4

The line segments are congruent.

The line segments are vertical, thus the slope of the line is undefined.

If opposite sides are equal and parallel, then the quadrilateral is a parallelogram.

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