1. A student enlarged this rectangle to fill as
much as possible of an 8.5 cm x 11 cm
piece of paper. What scale was used?
6.3 cm
4.7 cm
A 1.75
B 1 : 2.34
C 1 4.43
D 1 : 5.94

Answer:

5cm+6cm=11cm

Step-by-step explanation:

Adding the two,

The lower limit is 69.4 inches and the upper limit is 70.6 inches.

The 90% confidence interval for the mean height of all U.S. males can be calculated using the formula:

\(CI = \bar{x} \pm\(\dfrac{\sigma}{\sqrt{n}}\)

Here \(\bar{x}\) is the sample mean, σ is the population standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level.

For a 90% confidence level, z = 1.645.

Substitute the given values, and we get:

CI = 70 ± 1.645(1.5/√18)

CI = 70 ± 0.581

Lower limit = 70 - 0.581= 69.419

Upper limit = 70 + 0.581= 70.581

Therefore, the 90% confidence interval for the mean height of all U.S. males is [69.4, 70.6] inches.

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Answer:

obviously 8.4 is bigger than 2.4

Only table 1 represents the directly proportional relationship.

Given are the tables representing proportional relationship.

We can write the slope as -

{m} = (- 4 + 3)/(- 2 + 1) = 1

The equation will be -

y = x

Remaining tables does not show the direct variation.

Refer to the graph attached.

Therefore, only table 1 represents the directly proportional relationship.

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Answer:

its

A : Increase the sample size.

E : Decrease the confidence level.

Step-by-step explanation:

The formula that defines the sequence is f(n) = f(n-1) + 4

The recursive function rule is expressed as;

f(n) = f(n-1)  + d

where

d is the common difference

Given the following sequence

2, 6, 10, 14, 18..

Determine the common difference

d = 6-2 = 10-6

d = 4

Substitute to have

f(n) = f(n-1)  + d

f(n) = f(n-1) + 4

Hence the formula that defines the sequence is f(n) = f(n-1) + 4

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Answer:

Step-by-step explanation:

Given the system of equation;

kx - y = 2 ------------------- 1

6x - 2y = 3 -------------------- 2

Rewriting the equations in the format ax+by+c = 0

Equation 1 becomes kx - y - 2 = 0

Equation 2 becomes 6x - 2y - 3 = 0

where a₁ = k, b₁ = -1 and c₁ = -2  and a₂ = 6, b₂ = -2 and c₂ = -3

For the system of equation to have a unique solution the following must be true;

a₁/a₂ ≠ b₁/b₁

Substituting the coefficients into the condition, we will have;

k/6 ≠ -1/-2

k/6 ≠ 1/2

Cross multiplying we will have;

2k ≠ 6

k ≠ 6/2

k ≠ 3

This means that k can be any other real values except 3 for the system of equation to have a unique solution.

The inequality representing the given situation is -

300x + 700y ≤ 7500

Advertising is the practice and techniques employed to bring attention to a product or service. Advertising aims to put a product or service in the spotlight in hopes of drawing it attention from consumers.

Given is that Bobby Flay is deciding how to advertise a new gourmet restaurant that he is opening. An online ad costs $300, and a TV ad costs $700. He has $7,500 to spend on the ads.

We can write the inequality as -

300x + 700y ≤ 7500

where -

{x} - number of online ads posted

{y} - number of TV ads poste

Plot the inequality on the graph. The shaded region represents the possible number of advertisements of each category Bobby can use to advertise.

Therefore, the inequality representing the given situation is -

300x + 700y ≤ 7500

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Answer:

x=1/8

Step-by-step explanation:

Answer:

x=1/8

Step-by-step explanation:

Answer:

\(6d \: is \: same \: as \: 4d + 2d\)

Step-by-step explanation:

\(4d + 2d = 6d \\ pls \: mark \: as \: brainliest\)

Answer:

Number Students= 1,634

Step-by-step explanation:

Giving the following information:

In a survey at a local university, 62% of students say that they get less than the recommended eight hours of sleep per night.

Group= 4,300 students

To calculate the number of students that sleeps at least 8 hours, we need to use the following formula:

Students= 4,300*(1-0.62)

Students= 4,300*0.38

Students= 1,634

The reference angle for the angle with the measure 2x/3 is 54⁰

You should understand that a reference angle is the acute angle to a given angle.

The given angle is 2x/3

We should understand that since the angle has the variable x

= x + 2x/3 = 90⁰

Simplifying the fraction to have

(3x+2x)/3 = 90

Cross and multiply we have 5x=270⁰

Making x the subject

x= 270/5

x=54⁰

Therefore, the reference angle with the measure 2x/3 is = 54⁰

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Answer:

the range of the prices is $28

Step-by-step explanation:

the range is 38-10 so it’s 28

the answer should be : y=-2x+5

Answer:

M=0

Step-by-step explanation:

there you go almost sure it is

Answer:

rise/run=y2-y1/x2-x1

Step-by-step explanation:

(12,18)

(-15,-18)

Answer:

18+18/12+15= 36/27

or 4/3/ &  1 1/3

-Sumin <3

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

The height that you should drop an object in order for it to reach the ground in 12 seconds is; 2304 feet

We are told that time in the equation is represented by "t".

Now, for us to find the height, represented by "h", we will just plug in the given value in for t and simplify to find h.

Thus;

t = (1/4)√x

Plug in 12 for t to get;

12 = (1/4)√x

Multiply both sides by 4 to get;

48 = √x

Square both sides to get;

x = 2304 ft  

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

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Answer:

add them together and then u should get your answer

It is Called because 627 times 35 equals 21,945.

The linear function g which has a rate of change of -16 and initial value 600 is; g = -16x + 600.

It follows from the task content that the linear expression which is as described by the given verbal description is to be determined.

Since the standard slope-intercept form of a linear function is as given; f(x) = ax + b.

Where, a = slope (rate of change) and b = y-intercept (initial value).

Therefore, the required linear function which is as described is;

g = -16x + 600

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\(\\ \sf\longmapsto XY+YZ=XZ\)

\(\\ \sf\longmapsto 7a+5a=6a+24\)

\(\\ \sf\longmapsto 12a=6a+24\)

\(\\ \sf\longmapsto 12a-6a=24\)

\(\\ \sf\longmapsto 6a=24\)

\(\\ \sf\longmapsto a=\dfrac{24}{6}\)

\(\\ \sf\longmapsto a=5\)

Value of a is 4 and value of YZ is 20 units

Step-by-step explanation:

Given:

Y is between point X and Z

Value of line XY = 7a

Value of line YZ = 5a

Value of line XZ = 6a + 24

Find:

Value of "a" and line YZ

Computation:

We know that

XY + YZ = XZ

So,

7a + 5a = 6a + 24

12a = 6a + 24

6a = 24

a = 4

Value of a = 4

So,

Value of line YZ = 5a

By putting value of a

Value of line YZ = 5(4)

Value of line YZ = 20 units

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Answer:

P ($)=70-5(t)

Where p = price at t days

t = number of days

Step-by-step explanation:

The product price initially = $70

Now, every day , it reduces $5

The rate=$5 per day reduction

The price in the days will be determined by the formula below

P ($)=70-5(t)

Where p = price at t days

t = number of days

So let's assume it's on the second day

The price after the second day

P($) = 70-5(2)

P($) = 70-10

P($)= $60

The price after two days will be reduced to $60

Answer:

Step-by-step explanation:

The segment sum theorem tells you the whole is the sum of the parts. That can be used to write an equation for y.

  RS +ST = RT

  (5y +5) +(4y +8) = 67

Simplifying, we get ...

  9y +13 = 67

  9y = 54 . . . . . . . . subtract 13

  y = 6 . . . . . . . . . divide by 9

RS = 5y +5 = 5·6 +5 = 35

ST = 4y +8 = 4·6 +8 = 32

The values of interest are ...

The height of the skyscraper is D. 156.26 ft

To determine the height of the skyscraper,  we need to consider the following trigonometric identities listed thus;

From the information given, we have that;

Angle, θ = 38 degrees

The shadow casted is the adjacent side of the angle and is 200 ft

The height off the skyscraper is the opposite side

Now, using the tangent identity, we have that;

tan θ = opposite/adjacent

tan 38 = h/200

cross multiply the values, we get;

h = 200(0.7812)

Multiply the values

h = 156. 26 ft

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An equation that could be the equation of this parabola include the following: C. x = 1/12(y²).

In Mathematics, the standard equation of the directrix lines for any parabola that opens to the right is represented by this mathematical expression:

x = a(y - k)² + h.

Where:

By critically observing the graph which models the equation of this parabola, we can logically deduce that the vertex is at point (0, 0) and as such, we have the following:

h = 0

k = 0

a = positive.

x = a(y - k)² + h.

x = a(y - 0)² + 0.

x = ay²

Therefore, a possible equation is x = 1/12(y²).

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