Drag the numbers to complete the column two-way relative frequency table. Numbers may be used once, more than once, or not at all.

2829383949100
7th 8th Total
0–300 61%
% 50%
300+
% 62% 50%
Total
%
% 100%

Answer:

KL - slope 6/5 , length 7.8

LM - slope -5/6 , length 7.8

MN - slope 6/5 , length 7.8

NK - slope -5/6 , length 7.8

Step-by-step explanation:

square :3

The volume of the rectangular prism is 140 cubic meters

The volume of a figure is a measure of the amount of space it occupies in three-dimensional space. It is a scalar quantity, meaning that it is a single numerical value with no direction.

The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height.

This problem is a two rectangular prism joined together.

The volume can be calculated as;

V = l * w * h

v = (4 * 7 * 3) + (2 * 7 * 4)

v = 140m³

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From the table which represents the  exponential function , the multiplicative rate of change of function is (a) 1/5 .

The exponential function is expressed mathematically as : y = a(b)ˣ ;

where "a" is = initial value of function , and "b" is = multiplicative rate of change  ;

We first substitute , the first two values from the exponential table ;

we get ;

⇒ 2 = a(b)¹  

⇒ 2 = ab    ,...,,....equation(1) ;

Now substituting the second value ,

we get ;

⇒ 2/5 = a(b)²    ,....equation(2) ;

On dividing equation(2) by equation(1) ,

we get;

⇒ 2/(2/5) = ab/ab²  ;

⇒ 5 = 1/b ;

⇒ b = 1/5 .

Therefore , the multiplicative rate of change is b = 1/5 .

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The given  question is incomplete , the complete question is

The table represents an exponential function.

What is the multiplicative rate of change of the function ?

(a) 1/5

(b) 2/5

(c) 2

(d) 5

Answer:

2,19/3 this is answer this is correct

a) The table represents an exponential growth function.

b) The number of people that will have visited the website after 47 days online is given as follows: 17,716 people.

An exponential function is modeled as follows:

y = a(b)^x.

In which:

The parameters for this problem are given as follows:

Considering that the reference day is the day 42, the function is defined as follows:

y = 11000(1.1)^(x - 42).

Hence, after day 47, the number of visitors is given as follows:

y = 11000 x (1.1)^5.

y = 17,716.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let the time taken by Jeeny in both the cases be " t " ~

Now, during upstream : current flow opposes the flow of swimmer (Jenny)

Let her actual speed without current be " v ", so her speed in current (upstream) will be :

[tex]\qquad \sf  \dashrightarrow \: v - 1 \: \: kmph[/tex]

Now, according to formula :

[tex]\qquad \sf  \dashrightarrow \: distance = speed \times time[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8 = (v - 1)t \: \: \: \: \: - (1)[/tex]

Next, durijg dowstream : current flow supporta the flow of swimmer (Jenny)

So, her speed while going downstream will be :

[tex]\qquad \sf  \dashrightarrow \: v +1 \: \: kmph[/tex]

By same formula,

[tex]\qquad \sf  \dashrightarrow \: 16 = (v + 1)t \: \: \: \: \: - (2)[/tex]

Now, solve the two equations ~

[ since time taken by her in both the cases is same, we use t in both equations ]

Divide equation (1) by equation (2) :

[tex]\qquad \sf  \dashrightarrow \: \dfrac{8}{16} = \dfrac{v - 1}{v + 1} [/tex]

[ t gets canceled out ]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{2} = \dfrac{v - 1}{v + 1} [/tex]

[ cross multiply ]

[tex]\qquad \sf  \dashrightarrow \: v + 1 = 2(v - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v + 1 = 2v - 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2v - v = 1 - ( - 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = 1 + 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = 3 \: \: kmph[/tex]

That's the required answer ~ [ Jimmy would swim at the rate of 3 kmph if she there was no current ]

Step-by-step explanation:

-1 1/2 = -3/2

1/4 × (x - 2/5) = -3/2

let's multiply both sides by 4 to remove the first fraction on the left side :

x - 2/5 = -12/2

x = -12/2 + 2/5 = -6 + 2/5

-6 = -6 × 5/5 = -30/5

so,

x = -30/5 + 2/5 = -28/5 = -5 3/5 = -5.6

please pick any form you need for your result.

The true statement is (d) The area of triangle XYZ is equal to the area of triangle X'Y′Z

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

Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y'Z'.

The rotation is a rigid transformation

This means that it does not change the side length and angles of a shape when applies

Using the above as a guide, we have the following:

The image and the preiamage have the same area

Hence, the true statement is (d)

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Complete question

Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y′Z'.

y. z. y. x. x.

Which statement is true?

The sum of the angle measures of triangle XYZ is 90° less than the sum of the angle measures of triangle X'Y′Z'.

The angle measures of triangle XYZ are less than the corresponding angle measures of triangle X'Y′Z'.

Triangle XYZ is not congruent to triangle X'Y′Z'.

The area of triangle XYZ is equal to the area of triangle X'Y′Z

Answer:

Step-by-step explanation:

Let me explain each step in more detail.

Step 1: Calculate the Z-score

The Z-score is a measure of how many standard deviations a value is from the mean. To calculate the Z-score, we use the following formula:

Z = (x - μ) / σ

Where:

x = 9.8 ounces (the value we want to examine)

μ = 10.2 ounces (the mean of the distribution)

σ = 0.12 ounces (the standard deviation of the distribution)

Plugging in the values, we get:

Z = (9.8 - 10.2) / 0.12 = -3.33

This Z-score tells us that 9.8 ounces is 3.33 standard deviations below the mean of 10.2 ounces.

Step 2: Look up the cumulative probability from a Z-table

A Z-table is a table that lists the cumulative probabilities for various Z-scores. The cumulative probability tells us the probability of getting a value less than or equal to a certain Z-score. To use the Z-table, we need to know the Z-score and whether we want the cumulative probability to the left (for values less than) or to the right (for values greater than). In this case, we want the cumulative probability to the left because we want to find the probability of getting a weight less than or equal to 9.8 ounces.

The cumulative probability for a Z-score of -3.33 is approximately 0.0004. This means that there is a 0.0004 (or 0.04%) chance of getting a weight of 9.8 ounces or less in a bag of chips.

Step 3: Interpret the results

Since the cumulative probability is very small, it is highly unlikely that a bag of chips would contain 9.8 ounces or less of chips. Therefore, we can conclude that it is unusual for a bag of chips to contain 9.8 ounces or less.

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Answer:

Step-by-step explanation:

To find the solutions of the equation 24x² + 2x - 15 = 0, you can use the quadratic formula.

The quadratic formula states that given a quadratic equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0, the solutions are given by:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 24, b = 2, and c = -15, so:

x = (-2 ± √(2² - 4 * 24 * -15)) / 2 * 24

x = (-2 ± √(4 + 1440)) / 48

x = (-2 ± √(1444)) / 48

Taking the square root of both sides, we have:

x = (-2 ± 38.2) / 48

Therefore, the solutions are:

x = (-2 + 38.2) / 48 = 36.2 / 48 = 0.75

x = (-2 - 38.2) / 48 = -40.2 / 48 = -0.84

Since 0.75 > -0.84, the greater of the two solutions is 0.75.

Answer:

the answers are: 36/48

-40/48

Answer:8.64

Step-by-step explanation:

Answer:

8,64

Step-by-step explanation:

[tex]\frac{18}{100}[/tex]*48=8,64

Mr. Kazoo needs to buy 6 boards to complete his fencing as he can not buy exactly 5.71 boards.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables.

We can form numerical expressions from statements.

Given, Mr. Kazoo is planning to build a fence.

The gate is 40 inches wide.

Therefore, He needs to buy (40/7) = 5.71 boards.

But, He can not buy a board 0.71 part of the whole part, So he needs to buy 6 boards to complete his fencing.

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The graph of the points on a coordinate plane is added as an attachment

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

(0.5, -1.5) and (3,5) on the coordinate plane

The description of the points are:

Using the above as a guide, we have the graph as an attachment

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Answer:you never asked for like in what minutes or hours?

Step-by-step explanation:

The car, traveling at a speed 5 mph faster than the truck, will take more than 4.6 hours to be more than 23 miles ahead.

This question pertains to relative speed. When the car is traveling at 55 mph and the truck at 50 mph, the car is effectively moving away from the truck at (55 mph - 50 mph) = 5 mph. To calculate the time it will take for the car to be more than 23 miles ahead, we can use the formula: Time = Distance/Speed. So the time it would take is Time = 23 miles / 5 mph = 4.6 hours. Therefore, it will take the car more than 4.6 hours to be more than 23 miles ahead.

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The balance will be at least $1200 after 8.18 months, if you deposit $1000 in an account that pays 3.5% annual interest compounded monthly.

The result of earning interest on a principal amount as well as the accumulated interest from earlier periods is known as compound interest. It occurs when money is reinvested rather being paid out, allowing interest to be generated on the principle and accrued interest over the next month.

The balance of an account with an initial deposit of $1000 earning 3.5% annual interest compounded monthly will reach $1200 after 8.18 months.

To find the time it takes for the balance to reach $1200, we can use the formula for compound interest, A = P[tex](1 + r/n)^{nt}[/tex],

where P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = 1000, r = 0.035, n = 12 (because the interest is compounded monthly), and t is the unknown variable. We can rearrange the formula to solve for t:

t = (A/P) / (1 + r/n)

Plugging in the values, we get

t = (1200/1000) / (12(1 + 0.035/12))

which simplifies to

t = 8.18 months

Therefore, it will take 8.18 months for the balance of the account to reach $1200.

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The value of the trigonometric equation sin D = 0.923

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔBCD

Now , the measure of BC = 24

The measure of side CD = 10

So , the measure of hypotenuse BD = √ ( BC )² + ( CD )²

Substituting the values in the equation , we get

The measure of BD = √ ( 576 ) + 100

The measure of BD = √ ( 676 )

The measure of BD = 26

Now , from the trigonometric relations ,

sin θ = opposite / hypotenuse

Substituting the values in the equation , we get

sin D = 24 / 26

On simplifying the equation , we get

sin D = 0.923

Hence , the equation is sin D = 0.923

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The correct conclusion from the given percentage of students of different categories is option(c): Classical is the preferred music for 52 students.

What is meant by percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. It is frequently indicated by the percent sign, "%."

Given,

Total number of middle school students = 400

Percent of students who prefer rock = 13%

Percent of students who prefer hip hop = 25%

Percent of students who prefer pop = 35%

Percent of students who prefer classical = 13%

Percent of students who prefer jazz = 14%

Now we can find the number of students for each category.

Number of students who prefer rock = 13/100 * 400 = 52

Number of students who prefer hip hop = 0.25 * 400 = 100

Number of students who prefer pop = 0.35 * 400 = 140

Number of students who prefer classical = 0.13 * 400 = 52

Number of students who prefer jazz = 0.14 * 400 = 56

We can now look at different options.

a) This is false as hip-hop is preferred by 100 students.

b) Together Pop and jazz are preferred by 140+56 = 196, which is not more than half (200) of students. So this is false.

c)  This is true as classical is preferred by 52 students.

d) Together rock and hip hop are preferred by 52+100 = 152, which is not equal to 172. So this is false.

Therefore the correct conclusion from the given percentage of students of different categories is option(c).

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Answer: c

Step-by-step explanation:

I did the test and it’s right

No The triangles' are not congruent

The length of the corresponding sides should be equal and the length of sides is gotten using the equation:

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points A(2, -8), B(-5, -2), C(-7, 3); and ΔDEF: D(-9, 7), E(-11, 12), F(-2, 1) are calculated as follows:

AB =√{(-2 + 5)² + (-8 + 2)²} = 6.71

DE = √{(-9 + 1)² + (7 - 12)²} = 9.43

BC = √{(-5 + 7)² + (-2 - 3)²} = 5.39

EF = √{(-11 + 2)² + (12 - 1)²} = 14.21

AC = √{(2 + 7)² + (-8 - 3)²} =  14.21

DF = √{(-9 + 2)² + (7 - 1)²} = 9.22

Examining the figures showing the side lengths shows that the two triangles are not congruent

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Answer:

a. The number of ounces of oat flakes in the box is 15 ounces - a ounces, or 15 - a ounces.

b. The cost of the almonds (in cents) is 30 cents * a ounces, or 30a cents.

c. The cost of the oat flakes (in cents) is 15 cents * (15 - a) ounces, or 15 * (15 - a) cents.

d. The total cost of a box of Almond Oats (in cents) is the cost of the almonds plus the cost of the oat flakes, or 30a + 15 * (15 - a) cents.

Using an exponential function, it is found that the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year is given by:

P= 100%[([tex]1.03^{t}[/tex]) - 1]

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

An increasing exponential function is modeled by:

A(t)= A(0)[tex](1+r)^{t}[/tex]

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

As a percentage, the increase is modeled by:

P= 100%[[tex](1+r)^{t}[/tex] - 1]

In this problem, the growth rate is of r = 0.03, hence:

P= 100%[      [tex](1+0.03)^{t}[/tex]- 1]

P= 100%[[tex](1.03)^{t}[/tex]- 1]

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a ) Construction of stem and leaf display of the data is:

For n = 129 and with splint unit = 0.1, the stem and splint map of the given data on Shower- inflow rate( L/ min) is as follows

a stem-and-leaf display of the data.

   Stems                                                Leaves

       2                                                       28

       3                                                1344567789

       4                                                 01356889

       5                                          00001114455666789

       6                              0000122223344456667789999

       7                                     00012233455555668

       8                                                02233448

       9                                         012233335666788

      10                                             2344455688

      11                                                2335999

      12                                                     17

      13                                                      9

      14                                                     36

      15                                                  0035

      16                                                  None

      17                                                  None

      18                                                     3

b) From brume and splint map we note that minimal Shower inflow rate is2.2 whereas outside is18.3 L/ mim. farther typical or representative rate is7.0 L/min.

c) The display of data on steam and leaf chart shows that data is positively skewed means concentration of data on left side or lower value side is high as compared to other side.

d) Distribution is not symmetric rather very clear positive skew ness is observed through steam and leaf chart. Even distribution is Unimodal.

e) From steam and leaf chart is indicative to conclude that the highest observation 18.3 is outlier.

A stem and splint plot, also known as a stem and splint illustration, is a way to arrange data so that it's simple to see how constantly colorful feathers of values do. It's a graph that displays ordered numerical data. A stem and a splint are divided into each piece of data.

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Complete question:

The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses:

4.6 12.1 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1

11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5

7.5 6.2 5.8 2.8 3.4 10.4 9.8 6.6 3.7 6.4

8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.9 6.2

5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3

7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.3 7.2

5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2

8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7

5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6

10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6

7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3

9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2

8.3 3.1 4.9 5.0 6.0 8.2 6.3 3.8 6.0

(a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

Stems Leaves

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

(b) What is a typical, or representative, flow rate?

L/min

(c) Does the display appear to be highly concentrated or spread out?

highly concentrated, except for a few values on the positive sidehighly concentrated in the middle highly concentrated, except for a few values on the negative sidespread out

(d) Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?

Yes, the distribution appears to be reasonably symmetric.No, the data are skewed to the right, or positively skewed. No, the data are skewed to the left, or negatively skewed.No, the distribution of the values appears to be bimodal.

(e) Would you describe any observation as being far from the rest of the data (an outlier)?

Yes, the value 2.2 appears to be an outlier.Yes, the value 15.5 appears to be an outlier. Yes, the value 18.3 appears to be an outlier.No, none of the observations appear to be an outlier.

Answer:

4 would be the rate of change

Step-by-step explanation:

y=mx+b mx = slope

The slope represents the rate of change. Then the rate of change will be 4.

The product of two rational numbers is 1 . A . Rational number because multiplying two rational numbers is equivalent to the ratio of 3 . Two integers which is 1 . a rational number .

The product of two rational numbers is always a rational number. This is because a rational number is defined as a number that can be expressed as the ratio of two integers.

When you multiply two rational numbers, you are simply multiplying two ratios, which is still a ratio and therefore a rational number.

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The triangles given can be determined to be :

You can use the Pythagorean Theorem and its Converse to determine the type of triangle.

The Pythagorean Theorem and its Converse are basically :

c ² = a² + b ²   This is a right angled triangle

c ² > ( a² + b ² ) This is an obtuse triangle

c ² < ( a² + b ² )

The triangles are :

13 :

26 ² = 24 ² + 10 ²

676 = 676

Right - angled

14 :

20 ² = 13 ² + 6 ²

400 > 205

Obtuse triangle

15 :

17 ² = 16 ² + 3 ²

289 > 265

Obtuse triangle

16 :

32 ² = 29 ² + 24 ²

1, 024 < 1, 417

Acute triangle

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Answer: To solve this expression, we first need to simplify the terms in the denominator:

5 1/3 - 4 2/3 + 1 1/6 x 2

We can convert each fraction to a mixed number:

5 1/3 = 5 + 1/3

4 2/3 = 4 + 2/3

1 1/6 x 2 = 2 x 1/6 + 2 = 2 + 1/3

Now we can perform the subtraction:

(5 + 1/3) - (4 + 2/3) + (2 + 1/3)

= 5 + 1/3 - 4 - 2/3 + 2 + 1/3

= 5 + 1/3 - 4 + 2 + 1/3 + 1/3

= 7

So the denominator simplifies to 7.

Next, we simplify the numerator:

8 - (2/3)^2

We can first square the fraction:

(2/3)^2 = 4/9

Now we can perform the subtraction:

8 - 4/9

= 8 - 4/9

= 8 x 9/9 - 4/9

= 72/9 - 4/9

= 68/9

So the numerator simplifies to 68/9.

Finally, we divide the numerator by the denominator:

68/9 ÷ 7 = 9.71

So, the expression simplifies to 9.71.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's use the formula rate = cost/length to find the cost of one inch of wire. We know that 23 inches of wire cost 92 cents, so the rate of one inch of wire can be found by dividing 92 cents by 23 inches:

rate = cost/length = 92 cents/23 inches = 4 cents/inch

Now that we have found the rate of one inch of wire, we can use it to find the cost of 34 inches of wire. We simply multiply the rate by the length:

cost = rate * length = 4 cents/inch * 34 inches = 136 cents

So, 34 inches of wire will cost 136 cents.

Step-by-step explanation:

the trick is to find the "norm" rate, which is the rate for one unit.

from there we can get the rate for any number of units just by multiplying.

so,

23 in for 92 cents.

that means the rate is

23/92 = 23/(23×4) = 1/4

so, by dividing numerator and denominator by 23 (in this case it has an integer result also for the denominator) we get the price for 1 inch of wire : 4 cents.

so, 34 inches then have the length/price ratio (we multiply numerator and denominator by 34)

1/4 × 34/34 = 34/136

that means 34 inches cost 136 cents (= $1.36).

The area of the given parallelogram is 12 cm².

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

The formula to calculate the area of a parallelogram can thus be given as,

Area of parallelogram = b × h square units

where b is the length of the base and h is the height

According to the given parallelogram ABCD, we have

Length of the base b = 5 + 9 = 14 cm

The height h = 8 cm

Area of parallelogram = b × h

Area of parallelogram = 14 × 8

Area of parallelogram = 112 cm²

Thus, the area of the given parallelogram is 12 cm².

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The question seems incomplete, the missing figure has been attached below.

To find the distance between the man's starting point and his final position, we can use vector addition.

Let's call the man's starting point A and his final position B. We can represent the two legs of his journey as vectors A and B, respectively.

The first leg of his journey, due west, can be represented as a vector of magnitude 4 km in the -x direction.

The second leg of his journey, on a bearing of 197°, can be represented as a vector in the -x and -y direction. We can use trigonometry to find the components of this vector.

The x component of the vector can be found using the formula:

x = magnitude * cos(angle) = d * cos(197°)

The y component of the vector can be found using the formula:

y = magnitude * sin(angle) = d * sin(197°)

where d is the magnitude of the vector (the distance the man traveled in this leg of his journey).

To find the magnitude of the vector, we'll use the Pythagorean theorem:

d^2 = x^2 + y^2

We can substitute the x and y components we found above into this equation to find d:

d^2 = (d * cos(197°))^2 + (d * sin(197°))^2

d^2 = d^2 * (cos^2(197°) + sin^2(197°))

d^2 = d^2

d = sqrt(d^2) = sqrt(d^2)

So the magnitude of the vector is d.

Next, we can add the two vectors to find the total distance from the man's starting point to his final position:

distance = sqrt((4 - d * cos(197°))^2 + (d * sin(197°))^2)

This is the distance the man is from his starting point. To find the exact value, we would need to know the value of d. However, without that information, this is as far as we can take the calculation.