Darnell solved a system of equations by graphing. When he graphed the lines,
he saw that the two lines intersected. What should Darnell conclude about the
solution to this system of equations?
There are infinitely many solutions.
There is exactly one solution.
There are exactly two solutions.
There are no solutions.

Answer:

The total length of the two straight parts is 80 m x 2 = 160 m.

So, the length of the curved part of the track is 400 m - 160 m = 240 m.

Let the radius of the curved part of the track be "r".

Since there are two curves, each of length "l", in the track, the total length of both curves is 2l.

The length of one curved part can be given by the formula:

l = 2πr, where π is pi (approximately equal to 3.14).

So, 2l = 2 x 2πr = 4πr.

Therefore, 4πr = 240 m.

Dividing both sides by 4π, we get:

r = 240 m / (4π) = 240 / (4 x 3.14) = 15 m.

Hence, the radius of the curved part of the track on both sides is 15 m.

The equation of the line that passes through (18, 16) and has a slope of 11/8 is 8y = 11x - 70.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables. Depending on the facts at hand, there are different ways to find a line's equation. Several techniques include:

Form of point slope, Form of a slope-intercept, Two-point form for intercepting.

The point slope form is given as:

(y - y1) = m (x - x1)

The point is (18, 16) and the slope is 11/8.

Substituting the values we have:

y - 16 = 11/8 (x - 18)

8(y - 16) = 11(x - 18)

8y - 128 = 11x - 198

8y = 11x - 70

Hence, the equation of the line that passes through (18, 16) and has a slope of 11/8 is 8y = 11x - 70.

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The most precise of the measures given 44mm. Hence option B is the correct answer.

The closeness of measured values is referred to as precision. We require the lowest scale attainable to measure in order to measure a value accurately.

Different scales of measures are presented to us. Any of these scales can be used to calculate the distance between two places. But we need to utilize the lowest scale in order to acquire an exact measurement. The millimetre (mm) is the lowest used scale in the options, making the measurement

Thus for the given options the smallest and the precise measure is obtained at 44mm.

Hence option B is the correct answer.

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Answer:

A composite figure is made up of simple geometric shapes. To find the area of a composite figure or other irregular-shaped figure,divide it into simple, nonoverlapping figures. Find the area of each simplerfigure, and then add the areas together to find the total area of the compositefigure

Step-by-step explanation:bc of the way u gave it im showing it to u

The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function over the x-axis, shifting it left by 3 units, and down by 2 units.

To reflect a quadratic function over the x-axis, we need to multiply the function by -1. Let's assume that our original quadratic function is f(x).

After reflecting the function over the x-axis, we get the new function g(x) = -f(x).

To perform a horizontal shift left 3 units, we need to replace x with (x + 3) in the function g(x). This gives us the new function h(x) = g(x + 3) = -f(x + 3).

Finally, to shift the function down 2 units, we need to subtract 2 from the entire function h(x).

Note that the order of the transformations is important. We first reflect the function over the x-axis, then shift it horizontally, and finally shift it vertically.

Hence,

The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function

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Answer:

minimum is $14.40

maximum is $18

she can get 9 ice cream cups

Step-by-step explanation:

(1) The hypothesis is stated that completing a 2-week mindfulness training course

(2) The type of study design this is randomized controlled trial.

(3) The choice of the study type is randomized controlled trial is justified. (4) The list of the two variables with their operational definitions is 2-week mindfulness training course and GRE scores.

(5) Yes, this study demonstrate that the relationship between the two variables is causal

In a study conducted by Mrazek et al. (2013), it was found that students who completed a 2-week mindfulness training course scored higher on the GRE than those who did not participate in the training.

The hypothesis of this study is that completing a 2-week mindfulness training course will result in higher scores on the GRE compared to those who do not complete the training.

This study design is a randomized controlled trial. In this type of study, participants are randomly assigned to either a treatment or control group, and the effects of the treatment are compared to the effects of no treatment (or a placebo). In this case, the treatment group received the 2-week mindfulness training course, while the control group did not.

The choice of study type as a randomized controlled trial is justified because it allows for the comparison of two groups while minimizing the effects of confounding variables. Random assignment to groups helps to ensure that any differences in outcomes between the groups are due to the treatment and not some other factor.

The two variables in this study are the completion of the 2-week mindfulness training course and GRE scores. The operational definition of completion of the training course is that participants in the treatment group attended all sessions of the 2-week course. The operational definition of GRE scores is the score that participants received on the exam.

This study does suggest a causal relationship between completion of the mindfulness training course and higher GRE scores. The randomized controlled trial design helps to reduce the effects of confounding variables, making it more likely that any observed differences in outcomes between the treatment and control groups are due to the treatment.

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In a density curve, the proportion of data is represented by the option B) area under the curve and correct classification of shapes of density curves is option E)

A density curve is a curve on a graph that represents the distribution of values in a dataset.

A density curve, also called a density function, is a graphical representation of the relative frequency distribution of a continuous random variable. The type of distribution most commonly represented by a density curve is the normal distribution, but any distribution of a continuous variable may be represented by a density curve.

Normal distribution curve is a bell shaped curve obtained for the distribution having maximum frequency near the central value of distribution and the frequency gradually tapering off symmetrically on both side.so, All → Symmetric → Bell → Normal

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Step-by-step explanation:

sorry for the wait I hope this helps you with you're problem

Answer:

B. 5/22

----------------------

Total number of students is:

Probability of a first girl is 6 of 12:

Probability of a second girl is 5 of 11 since both numbers reduced by one:

Probability of the two events is:

Correct choice is B.

Answer:

y=5

divide 40 by 8

times 5 by 8 to check your solution

Answer:

see explanation

Step-by-step explanation:

40 = 8y ( isolate y by dividing both sides by 8 )

5 = y

As a check

substitute y into the right side of the equation and if both sides are equal then it is the solution.

right side = 8y = 8 × 5 = 40 = left side

since both sides are equal then y = 5 is the solution to the equation

Answer:

10) m∠2 = 139°

11) m∠3 = 139°

12) m∠4 = 41°

Step-by-step explanation:

Question 10

∠2 and the adjacent angle of 41° are supplementary angles since they lie on opposite sides of the same line; they must add up to 180°

m∠2 + 41° = 180°

m∠2 = 180-41 =139°

Question 11

∠2 and ∠3 are formed by the intersection of two rays. They are vertically opposite angles and therefore they must be equal

m∠3 = m∠2 = 139°

Question 12

Angles  ∠3 and ∠4 are supplementary angles (same reasoning as q 10)

Therefore m∠4 = 180°  - m∠3

= 180° - 139° = 41°

Note that there are many ways to arrive at the answers for m∠4

The missing side length is x = 30

What are basic Trigonometric functions?

The angles of sine,  cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.

In a Right-angled triangle, the tan of an angle is equal to the opposite side/adjacent side

from the given figure,

tan 37° = x/40

0.75 = x/40

x = 30

Therefore, The missing side is 30.

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a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. G(Diego) =5

A relation is a function if it has only One y-value for each x-value.

Given that a  Function G takes a student's first name for its input and gives the number of letters in the first name for its output.

a.

Given that G(Jada) = 4

In the above function Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. We need to find the value of G(Diego)

In the above function Diego is the input and 5 will be output, the output is 5 because there are 5 letters in Diego word.

G(Diego) =5

Hence, a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. G(Diego) =5

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The surface area is changing at a rate of approximately 2.94 square meters per second when the volume is 36 cubic meters and the balloon is being inflated at 3 cubic meters per second.

Volume of a sphere in terms of its radius = V = (4/3)π[tex]r^3\\[/tex]     .......(1)

Differentiating on both sides,                       [tex]\frac{dV}{dt}[/tex] = 4π[tex]r^{2}[/tex][tex]\frac{dr}{dt}[/tex]      .......(2)      

r = radius of the sphere.

Spherical balloon is being inflated at a rate of 3 cubic meters per second.

[tex]\frac{dV}{dt}[/tex] = 3 [tex]m^3/sec[/tex]

Volume is 36 cubic meters.

V = 36 [tex]m^3[/tex]

From equation (1), [tex]r^3[/tex] = [tex]\frac{3V}{4\pi }[/tex]

                              [tex]r^3[/tex] = [tex]\frac{3*36}{4*\pi }[/tex]

                              [tex]r^3\\[/tex] = [tex]8.59^1^/^3[/tex]

                               r = 2.04 meters

Substituting this in equation (2),  [tex]\frac{dr}{dt}[/tex]  =   [tex]\frac{dV}{dt}[/tex] / 4π[tex]r^{2}[/tex]

                                                     [tex]\frac{dr}{dt}[/tex]  =   3/(4π[tex]2.04^{2}[/tex])

                                                     [tex]\frac{dr}{dt}[/tex]  =   0.05737 m/sec

Now, surface area of sphere = A = 4π[tex]r^{2}[/tex]

Differentiating on both sides,

Rate of change of surface area  [tex]\frac{dA}{dt}[/tex] = [tex]8\pi r\frac{dr}{dt}[/tex]

                                                       = 8* 3.14* 2.04* 0.05737

                                                       = 2.94 [tex]m^2/sec\\[/tex]

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Answer: hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

Answer: pay attention

Step-by-step explanation:

Answer:

SOLVE IT!

Step-by-step explanation:

A. 45.50+0.11= answer

B. 65.50+0.17= answer

Minus A plus B to get answer!

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

ghjhkvfgfgnfdgn

The volume of a cylinder can be calculated as π * radius^2 * height. In this case, the radius is 0.5 ft and the height is 25 ft, so the volume is:

π * 0.5^2 * 25 = 19.63 cubic feet

So the cost of the utility pole would be 19.63 * $25.81 = $509.24

Rounding to the nearest cent, the cost of the utility pole would be $509.24, which can be rounded to $509.00.

The missing value is given as follows:

x = 11.3 cm.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The parameters for this problem are given as follows:

Hence the missing value is obtained as follows:

14² + x² = 18²

x = sqrt(18² - 14²)

x = 11.3 cm.

We have a triangle in which:

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Answer:

First, we need to find the area of Site A and Site B. The area of a rectangle is found by multiplying its length and width, so:

Site A: 60 m x 40 m = 2400 m^2

Site B: 45 m x 40 m = 1800 m^2

Next, we need to find the perimeter of each site, which is the distance around the edges of the rectangle. The perimeter is found by adding up the lengths of all four sides, so:

Site A: 2 x (60 m + 40 m) = 2 x 100 m = 200 m

Site B: 2 x (45 m + 40 m) = 2 x 85 m = 170 m

Finally, to find the total amount of rope needed, we add up the perimeters of both sites:

200 m + 170 m = 370 m

So, we need a total of 370 meters of rope to rope off both sites.

Answer:350

ITS NOT 370

The algebraic expression G x C, where G represents the total number of gallons needed and C represents the cost per gallon.

In mathematics, an expression is a combination of one or more numbers, variables, and/or operators that represent a quantity or a mathematical relationship.

To calculate the total cost of gasoline, we first need to determine how many gallons of gasoline will be needed for the entire trip. This can be done by dividing the total distance traveled by the car's miles per gallon (MPG) rating. Let's use "G" to represent the total number of gallons needed.

G = Total Distance Traveled / MPG

To find the total cost of gasoline, we can multiply the number of gallons needed by the cost per gallon. Let's use "T" to represent the total cost of gasoline.

T = G x C

Using the expression we developed earlier, we can now find the total cost of gasoline for the full-size car:

=> T = G x C

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Complete Question:

Four friends plan to rent a car to go on a camping trip. They will drive a total of 450 miles. The cost of gasoline is $2.20 per gallon Type of Car SUV Full size Compact Rental Cost $283 $215 $183 Insurance Cost $120 $108 $95 Miles per Gallon 24 25 33 Total Gas Cost $ $ $ Cost per Person.

Write an algebraic expression for the total cost of the gasoline.

The area of an equilateral triangle is 16√3 m² and the perimeter of an equilateral triangle is 24 m.

In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4 ×a².

From the given figure, side of the equilateral triangle is 8 m.

Now, area of an equilateral triangle is

√3/4 ×8²

= √3/4 ×64

= 16√3 m²

The perimeter of an equilateral triangle is 3a.

Now, the perimeter is 3×8

= 24 m

Therefore, the area of an equilateral triangle is 16√3 m².

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To buy down the quoted interest rate from 4.75% to 4.5% will cost Trystan and Kendall $4,800 after the down payment.

The down payment refers to the initial cash payment for the purchase of an item on mortgage.

The down payment is required by the financier to evaluate the buyer's financial readiness.

The cost of the new home = $300,000

Down payment = 20% or $60,000 ($300,000 x 20%)

Mortgage loan required = $240,000 ($300,000 - $60,000)

Bank quoted interest rate = 4.75%

Desired interest rate = 4.5%

Difference in interest rate = 0.25% (4.75% - 4.5%)

Rate of buy down of the quoted interest per point = 0.125%

The number of points to buy down the interest rate = 2 (0.25/0.125)

The cost of each point = 1% of $240,000 = $2,400

The total cost of 2 points = $4,800 ($2,400 x 2)

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Answer: 159 bpm

Step-by-step explanation:

if his rate is 53 beats in 1/3 of a minute, in 3/3 of a minute, (1 full minute), it will be 53 x 3 = 159 beats

so we can say his heart rate is 159 beats/minute, or 159 bpm

Answer:

8a3

Step-by-step explanation:

volume of cube = Lcube

one side=length of cube

so

volume of cube= L3

=2a3

= 2A × 2A × 2A