Write the word sentence as an equation. Then solve.

The quotient of a number x and −1.5 is 21.

Equation:

Question 2
Solution: x=

Answer:

128 dollars

Step-by-step explanation:

hope it helped! :)

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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The solution of the given system of equations using the matrix method and elementary transformations are x = -1, y = 3, z = 1/2

Let's represent the given system of equations in matrix form.

{| 2 2x - y + 3z x + 2y - z |, | -4x + 5y + z 10 |, | 4 5 0 |}

To apply elementary row transformations, we can perform operations on the matrix to simplify and solve the system.

Multiply the first row by 2:

{| 4 4x - 2y + 6z 2x + 4y - 2z |, | -4x + 5y + z 10 |, | 4 5 0 |}

Add the second row to the first row:

| 4 4x - 2y + 6z 2x + 4y - 2z |

| 0 3y + 2z 10 |

| 4 5 0 |

Multiply the second row by (1/3):

| 4 4x - 2y + 6z 2x + 4y - 2z |

| 0 y + (2/3)z (10/3) |

| 4 5 0 |

Subtract the first row from the third row:

| 4 4x - 2y + 6z 2x + 4y - 2z |

| 0 y + (2/3)z (10/3) |

| 0 -4x - 6y + 4z -2x - 5y + 2z |

Divide the third row by -2:

| 4 4x - 2y + 6z 2x + 4y - 2z |

| 0 y + (2/3)z (10/3) |

| 0 2x + 3y - 2z x + (5/2)y - z |

Now, the system of equations can be rewritten as:

4x - 2y + 6z = 2x + 4y - 2z

y + (2/3)z = (10/3)

2x + 3y - 2z = x + (5/2)y - z

By Simplifying further:

2x - 6y + 8z = 0

3y + 2z = 10

x + (1/2)y - z = 0

Let us use substitution and elimination method, to solve the equations,

From the second equation, we can solve for y:

3y + 2z = 10

3y = 10 - 2z

y = (10 - 2z) / 3

Substituting this value of y into the third equation:

x + (1/2)((10 - 2z) / 3) - z = 0

x + (5 - z) / 3 - z = 0

x + 5/3 - z/3 - z = 0

x - (4/3)z + 5/3 = 0

x = (4/3)z - 5/3

Now, we can substitute the expressions for x and y into the first equation:

2x - 6y + 8z = 0

2((4/3)z - 5/3) - 6((10 - 2z) / 3) + 8z = 0

(8/3)z - 10/3 - (20 - 4z) + 8z = 0

(8/3)z - 10/3 - 20 + 4z + 8z = 0

(20/3)z - 10/3 = 0

20z - 10 = 0

20z = 10

z = 10/20

z = 1/2

Substituting this value of z back into the expressions for x and y:

x = (4/3)(1/2) - 5/3

x = 2/3 - 5/3

x = -3/3

x = -1

y = (10 - 2(1/2)) / 3

y = (10 - 1) / 3

y = 9/3

y = 3

Therefore, the solution to the system of equations is:

x = -1

y = 3

z = 1/2

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Answer: $79.95

Step-by-step explanation:

65 × 0.18 = 11.7

65 × 0.05 = 3.25

11.7 + 3.25 = 14.95

14.95 + 65 = $79.95

Answer:

If two secant segments intersect outside a circle, then the product of the secant segment with its external portion equals the product of the other secant segment with its external portion.

45(45) = (2x + 75)(27)

2,025 = (2x + 75)(27)

2x + 75 = 75, so x = 0 and GH = 48

Answer: y = 4x - 16

Step-by-step explanation:

Using the point slope formula to plug in your point and slope, I found

y - 4 = 4 (x - 5)

After simplifying it into an equation of the line I got  y = 4x - 16

The surface area of cylinder is  132\(\pi in^2\).

What is surface area ?

A two-dimensional flat surface's area is the space it takes up in space. It has a square unit of measurement. A three-dimensional object's surface area is the space it takes up when viewed from the outside. Square units are used to measure it as well.

Here in given cylinder Radius= 6 in and height = 5 in

Now using surface area formula for cylinder,

Surface Area = 2\(\pi\)r(r+h) square unit.

=> Surface area = \(2\times\pi\times6(6+5)\)

=> Surface area = 132\(\pi in^2\)

Hence the surface area of cylinder is  132\(\pi in^2\).

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Given:

The expression is

\(9-3\div \dfrac{1}{3}+1\)

To find:

The value of given expression.

Solution:

We have,

\(9-3\div \dfrac{1}{3}+1\)

BODMAS : Bracket, Order, Division, Multiplication, Addition, and Subtraction.

Using BODMAS, first we need to perform division in the given expression.

\(=9-(3\div \dfrac{1}{3})+1\)

\(=9-(3\times 3)+1\)

\(=9-9+1\)

Now, apply addition.

\(=(9+1)-9\)

\(=10-9\)

Now, apply subtraction.

\(=1\)

Therefore, the value of given expression is 1.

answer:

0.08 percent as a ratio is: 8/100

explanation:

hope this helped <3 also if wouldn't mind could you pls give me brainliest? (im trying to level up) thanks! :)

Answer:

8/100

simplest form 2/25

Step-by-step explanation:

Answer:

60/96

Step-by-step explanation:

Answer:

10:16 or 2.5:4

Step-by-step explanation:

sorry if i am wrong

The 90% confidence interval is: (2.51, 3.22)

It is a boundary of values which is eventually to comprise a population value with a certain degree of confidence. It is usually shown as a percentage whereby a population means lies within the upper and lower limit of the provided confidence interval.

We have the following information :

The level of significance is calculated as:

\(\alpha =1-c\\\\\alpha =1-0.90\\\\\alpha =0.10\)

The degrees of freedom for the case is:

df = n - 1

df = 15 - 1

df = 14

The 90% confidence interval is calculated as:

=x(bar) ±\(t_\frac{\alpha }{2}\), df \(\frac{s}{\sqrt{n} }\)

= 2.86 ±\(t_\frac{0.10 }{2}\), 14 \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 1.761 × \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 0.3547

= (2.51, 3.22)

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Step-by-step explanation:

Using the given formula, we can substitute x = 3 and solve for y:

y = 5 x 2^x

y = 5 x 2^3 (substitute x = 3)

y = 5 x 8

y = 40

Therefore, when x = 3, y = 40.

Answer:

y = 40

Step-by-step explanation:

Plug in 3 for x

\(\bf{y=5\times2^x}\)

\(\bf{y=5\times2^3}\)

Simplify

\(\bf{y=5\times8}\)

Simplify

\(\bf{y=40}\)

Hence, y = 40

Answer:

there are no solutions to m

Step-by-step explanation:

\( - 2(m + 4) - 9 = \\ 5 - 2(m + 4) - 9 = 5\)

\( - 2m - 8 - 9 = 5 - 2m - 8 - 9 = 5\)

\( - 2m - 17 = - 2m + 5 - 8 - 9 = 5\)

\( - 2m - 17 = - 2m - 3 - 9 = 5 \)

\( - 2m - 17 = - 2m - 12 = 5\)

\( - 2m = - 2m + 5 = 5\)

\( - 2m = - 2m + 5 = 5 \\ - 2m = - 2m = 0 \\ - 2m = m = 0 \\ - 2(0) = 0 \\ 0 = 0\)

check

\( - 2(0 + 4) - 9 = 5 \\ - 2(0 + 4) - 9 = 5 \\ \\ 0 - 8 - 9 = 5 \\ 0 - 8 - 9 = 5 \\ - 17 = 5 \\ there \: are \: no \: solutions\)

Answer:

\((x - \frac{ - 9 + \sqrt{161} }{2} )(x - \frac{ - 9 - \sqrt{161} }{2} ) \)

Step-by-step explanation:

\(1. \: a(x - \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} ) \: (x - \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a}) \\ 2. \: (x - \frac{ - 9 + \sqrt{ {9}^{2} - 4 \times - 20 } }{2} ) \: (x - \frac{ - 9 - \sqrt{ {9}^{2} - 4 \times - 20 } }{2} )\)

Answer:

6 ft

Step-by-step explanation:

Since the shape of the cables on the bridge are to open up, the standard equation of the parabola produced is given as:

(x - h)² = 4p(y - k)

Where (h, k) is the vertex and focus is at (h, k+p)

From the question, the point (0, 2) is the vertex and point (50, 27) lie on the parabola. Hence:

(x - 0)² = 4p(y - 2)

x² = 4p(y - 2).

Sinc the tower is 100 ft apart and 27 ft height, hence the point 100/2 = 50 ft and 27 ft lie on the parabola

To find p, use (50, 27)

50² = 4p(27 - 2)

2500 = 4p(25)

100p = 2500

p = 25

hence:

x² = 4(25)(y - 2)

x² = 100(y - 2)

At a point of 20 feet (i.e x = 20), y is the height of the cable, hence:

20²=100(y-2)

400 = 100y - 200

100y = 600

y = 6

The height is 6 ft at a point of 20 ft

They requried two examples where (2) (3) triangles can be found in building construction Roof trusses and Concrete forms.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
Two examples of where (2) (3) triangles can be found in building construction are:

Roof Trusses: Roof trusses are a common feature in building construction and are made up of a series of triangles. The truss is composed of a top chord, a bottom chord, and diagonal members that connect the two chords to form triangles. The triangles in the truss provide strength and stability to the roof structure.

Concrete Forms: Concrete forms are used to shape poured concrete into various shapes and sizes. Triangular forms are commonly used to create structures such as columns and walls. The triangular shape of the form helps to distribute the weight of the wet concrete evenly, ensuring that the final structure is strong and stable.

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The question seems to be incomplete, complete question is given as,
which type of triangle is commonly used in building constructions, list any two examples where (2) (3) Triangles one can find them​.

Answer:

x=-1

Step-by-step explanation:

Step 1: Subtract x from both sides.

−x+4−x=x+6−x

−2x+4=6

Step 2: Subtract 4 from both sides.

−2x+4−4=6−4

−2x=2

Step 3: Divide both sides by -2.

−2x/−2= 2/−2

x=−1

Hope this helped :)

Answer:

2m-8+1=2m-7

Step-by-step explanation:

Slack represents the buffer or flexibility available in the project schedule, allowing for adjustments and potential delays without affecting the project's critical path.

In project network analysis, slack refers to the difference between the latest start and earliest start times of an activity. It represents the amount of time that an activity can be delayed without affecting the overall project duration.

The latest start time (LS) is the latest point in time an activity can start without delaying the project completion. It is determined by considering the dependencies and constraints of the project schedule. The earliest start time (ES) is the earliest possible point in time an activity can start based on its dependencies and the project schedule.

By subtracting the earliest start time from the latest start time, we calculate the slack or float of an activity. If an activity has positive slack, it means there is flexibility in its start time, and it can be delayed without impacting the project's critical path or completion date. On the other hand, if the slack is zero or negative, it indicates that any delay in the activity will affect the project's overall duration, making it critical.

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Answer:

90.78%

Step-by-step explanation:

So the 100% value of the car=$28500

We don't know the percentage ?% =$25875

So 25875/28500×100=90.78%

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

The speed of the rock just before it strikes the ground is given by v = √(2 * 9.8 m/s² * h), where h is the height from which the rock falls.

To calculate the kinetic energy gained by the rock while falling, we need to determine the change in potential energy. The potential energy lost by the rock is converted into kinetic energy.

The potential energy lost by the rock is given by the formula: ΔPE = m * g * h, where m is the mass of the rock (2.2 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height from which the rock falls.

Since the rock starts from rest, its initial kinetic energy is zero. Therefore, the change in kinetic energy is equal to the change in potential energy.

Using the conservation of energy principle, the change in potential energy is equal to the gained kinetic energy: ΔKE = ΔPE.

Now, we can calculate the gained kinetic energy: ΔKE = 2.2 kg * 9.8 m/s² * h.

To find the speed of the rock just before it strikes the ground, we can equate the gained kinetic energy to the final kinetic energy using the formula: KE = (1/2) * m * v², where KE is the kinetic energy, m is the mass of the rock, and v is the velocity or speed of the rock.

Setting ΔKE equal to KE and solving for v, we have: 2.2 kg * 9.8 m/s² * h = (1/2) * 2.2 kg * v².

Simplifying the equation, we get: v² = 2 * 9.8 m/s² * h.

Taking the square root of both sides, we find: v = √(2 * 9.8 m/s² * h).

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The minimum yield value of the key material should be determined based on the yield stress of the shaft, which is 36 kg/m², the dimensions of the key, and the safety factor of 2.

To ensure that the key smoothly transmits the torque of the shaft, it is essential to choose a key material with a minimum yield value that can withstand the applied forces without exceeding the yield stress of the shaft.

The dimensions of the key given are 20x20x120 mm. To calculate the torque transmitted by the key, we need to consider the dimensions and the applied forces. However, the specific values for the applied forces are not provided in the question.

The safety factor of 2 indicates that the material should have a yield strength at least twice the expected yield stress on the key. This ensures a sufficient margin of safety to account for potential variations in the applied forces and other factors.

To determine the minimum yield value of the key material, we would need additional information such as the expected torque or the applied forces. With that information, we could calculate the maximum stress on the key and compare it to the yield stress of the shaft, considering the safety factor.

Please note that without the specific values for the applied forces or torque, we cannot provide a precise answer regarding the minimum yield value of the key material.

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Answer:

Explanation:

The price of the refridgerator = $748

If there is a 65% mark-up, then we the selling price will be:

Answer:

The equivalent of given expression can be \(9.2\times(12+10.4)\) or \(9.2\times22.4\) or \(206.08\).

Step-by-step explanation:

The given expression is \((9.2\times12) + (9.2\times10.4)\).

Here, once can take 9.2 common from each bracket and write new expression and can also solve for final value of the expression.

The expression can be rewritten as,

\((9.2\times12) + (9.2\times10.4)=9.2\times(12+10.4)\\(9.2\times12) + (9.2\times10.4)=9.2\times22.4\\(9.2\times12) + (9.2\times10.4)=206.08\)

The above three expressions are the equivalent of the given expression.

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9514 1404 393

Answer:

  angle BAC = 35°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of the arc it intercepts. Arc BC is 70°, so inscribed angle BAC is half that, or 70°/2 = 35°.

_____

In this geometry, you can find angle BAC a couple of ways.

Any triangle inscribed in a semicircle is a right triangle. That is, AB is a diameter, so angle ACB intercepts half the circle (180°). Half that measure is 90°. Then angles ABC and BAC are complementary:

  angle BAC = 90° -55° = 35°

8x³ is a term

-5 is a coefficient

+ 7 is a constant

Algebraic expressions are defined as expressions that are made up of terms, variables, constants, factors and coefficients.

These algebraic expressions are also composed of arithmetic or mathematical operations.

These operations are;

From the information given, we have that the algebraic expression is;

8x³ - 2x - 5x+7

We have that;

8x³ is a term

-2x is a term

-5 is a coefficient

+ 7 is a constant

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Answer:

585m

Use the Pythagoreas' Theorem.

You will get the answer 585. Hope this helps!

Answer:

585m

Step-by-step explanation:

Answer gotta be 585m.

Answer:

0.06245

Step-by-step explanation:

Decrease 7/12=0.583

from 9 p.m to 6:20 am is 9:20= (9+20/60) = 9.33 hours

0.583/9.33 = 0.06248

round the 0.06248 to 0.06245