Which of these shapes are congruent

Monthly interest payment is $100.

According to the statement

balance in account = $100

APR = 12%

we use the formula Balance formula to solve this problem.

So, BALANCE * [APR / 12 month] to find monthly interest payment

Here balance is the starting amount in the bank account

And APR is the type of interest rate applied on the amount

And 12 month is the time period for which APR is applicable.

So, substitute the values in it then

Monthly interest payment = 100 * [12/12]

After solving the equation become

Monthly interest payment = 100*1

Monthly interest payment = 100$

So, Monthly interest payment is $100.

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The boat speeds of 15 km/h and 18 km/h, directions, and the time of travel of 45 minutes gives the angle between their paths as approximately 68°.

The given parameters are;

Direction of the first boat = Northeast

Speed of the first boat = 15 km/h

Direction of the second boat = Northwest

Speed of the second boat = 18 km/h

Distance between the boats after 45 minutes = 14.0 km.

45 minutes = 0.75 × 1 hour

Distance traveled by the first boat in 45 minutes, d1, is therefore;

d1 = 15 km/h × 0.75 hr = 11.25 km

For the second boat, we have;

d2 = 18 km/h × 0.75 hr = 13.5 km

Using cosine rule, we have;

14² = 11.25² + 13.5² - 2 × 11.25 × 13.5 × cos(A)

Where A is the angle between the paths of the two boats.

Which gives;

[tex]cos(A) = \frac{361}{972} [/tex]

[tex] A= \mathbf{ arccos\left(\frac{361}{972} \right) }\approx 68^\circ [/tex]

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[tex]\\ \rm\dashrightarrow B=10log\dfrac{I}{I_o}[/tex]

[tex]\\ \rm\dashrightarrow B=10\log\dfrac{10^{-7}}{10^{-12}}[/tex]

[tex]\\ \rm\dashrightarrow B=10log10^5[/tex]

[tex]\\ \rm\dashrightarrow B=10\times 5log10[/tex]

[tex]\\ \rm\dashrightarrow B=10(5)[/tex]

[tex]\\ \rm\dashrightarrow B=50dB[/tex]

Answer:

50 Db

Step-by-step explanation:

Given:

[tex]L=10 \log \dfrac{I}{I_0}[/tex]

[tex]I_0=10^{-12}[/tex]

where:

To find the approximate loudness of a dinner conversation with a sound intensity of [tex]I=10^{-7}[/tex], substitute the values of I and I₀ into the given equation and solve for L:

[tex]\implies L=10 \log \dfrac{10^{-7}}{10^{-12}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies L=10 \log 10^{-7-(-12)[/tex]

[tex]\implies L=10 \log 10^5[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies L=5 \cdot 10 \log 10[/tex]

[tex]\implies L=50 \log 10[/tex]

As the given log does not have a specified base, assume the base is 10.

[tex]\implies L=50 \log_{10} 10[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies L=50 (1)[/tex]

[tex]\implies L=50\:\:\sf Db[/tex]

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We conclude that the odds of hitting the ball are 0.158

The odds (like the probability) are given by the quotient between the number of attempts in which you hit the ball and the total number of attempts.

Here we know that out of 19 attempts, in 3 you hit the ball. Then the odds of hitting the ball are:

P = 3/19 = 0.158

We conclude that the odds of hitting the ball are 0.158

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The reason why the standard deviation of a set of data is always given as a positive number is because the individual values are squared.

The term standard deviation is used to express how much numbers depart from the mean value. Now we know that the standard deviation for each of the data points is the square of the difference between the score and the mean.

Given that the value that is extracted from each data point is squared, the standard deviation of a set of data is always given as a positive number, but data points can have a negative overall standard deviation.

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Answer:

1. Becky's rate of sales is 9 cups per hour

2. Mayisha's rate of sales is 10 cups per hour

3. Becky is selling 1 fewer cups per hour than Mayisha

4. Becky started with 2 fewer cups than Mayisha

Step-by-step explanation:

1. 30-12=18 18/2=9

2. 31-21=10 21-11=10

3. 10-9=1

4. 30+9=39 31+10=41 41-39=2

Answer:

Becky's rate of sales is [tex]\boxed{\sf 9}[/tex] cups per hour.

Mayisha's rate of sales is [tex]\boxed{\sf 10}[/tex] cups per hour.

Becky is selling [tex]\boxed{\sf 1\: fewer}[/tex] cup(s) per hour than Mayisha.

Becky started with [tex]\boxed{\sf 2}[/tex] fewer cups than Mayisha.

Step-by-step explanation:

Mayisha

[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 31 & 21 & 11\\\cline{1-4} \end{array}[/tex]

Becky

[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 30 & & 12\\\cline{1-4} \end{array}[/tex]

Selling at a steady rate.

To calculate the rate of sales, use the rate of change formula:

[tex]\sf Rate\:of\:change = \dfrac{change\:in\:y}{change\:in\:x}[/tex]

Therefore:

[tex]\textsf{Becky's rate of sales}=\dfrac{12-30}{3-1}=-9[/tex]

Therefore, as the number of cups reduces by 9 each hour, Becky's rate of sales is 9 cups per hour.

[tex]\textsf{Mayisha's rate of sales}=\dfrac{11-31}{3-1}=-10[/tex]

Therefore, as the number of cups reduces by 10 each hour, Mayisha's rate of sales is 10 cups per hour.

As 9 is one less than 10, Becky is selling 1 fewer cup(s) per hour than Mayisha.

As Becky had 30 cups left after 1 hour, and her rate of sales is 9 cups, then she started with 30 + 9 = 39 cups.

As Mayisha had 31 cups left after 1 hour, and her rate of sales is 10 cups, then she started with 31 + 10 = 41 cups.

As 39 is 2 less than 41, Becky started with 2 fewer cups than Mayisha.

The equation that represents the situation is,

y = x + 15

Given Information

It is given  that the students complete a 15-point extra-credit assignment in order to raise their test scores.

The new test score is 15 more than the old test score.

We have to find an equation for this situation. A mathematical equation is a formula that uses the equals sign to connect two expressions in order to express their equality.

Forming Equation

Original Score = x

New Score = y ................... (1)

Thus, after the test, the score is raised by 15 points.

⇒ New score = x + 15 .................... (2)

The following equation can be deduced from (1) and (2)

y = x + 15

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The Number of teams is  mathematically given as

N= 30100

Generally, the equation for Number of teams is  mathematically given as

X items are selected from n items by [tex]^nC_x[/tex] ways

[tex]^nC_x = \frac{n!}{ [ (n-x)! * x! ]}[/tex]

Number of teams

N= n(1 child and 3 adults) + n(2 child and 2 adults) + n(3 child and 1 adults) + n(4 child)

N= 16C1 * 15C3 + 16C2 * 15C2 + 16C3 * 15C1 + 16C4 * 15C0

N= 16 * 455 + 120 * 105 + 560 * 15 + 1820

N= 30100

In conclusion, the Number of teams

N= 30100

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Answer:

y = -1.3x + 10

Step-by-step explanation:

x_avg = (-2 + -1 + 1 + 2 + 3 + 4)/6 = 1.166666...

y-avg = (21 + 8.6 + 1 + 1 + 5 + 14.3) = 8.48333...

x      y       x-x_avg       y-y_avg          (x-x+avg)²           (x-x_avg)(y-y_avg)

-2    21     -3.1666        12.51666       10.02777                    -39.63611

-1    8.6     -2.1666        0.11666        4.69444                     -0.252777

1      1        -0.1666       -7.48333        0.02777                     1.247222

2      1       0.83333     -7.48333         0.69444                    -6.236111

3      5       1.8333        -3.48333        3.3611111                     -6.386111

4     14.3    2.8333        5.81666         8.02777                     16.480555

sum of (x-x_avg)(y-y_avg) = -34.858

sum of (x+x_avg)² = 26.8333

slope = [(x-x_avg)(y-y_avg)/[(x+x_avg)²]

slope = -34.858/26.8333

slope = -1.29907

y = mx + b

y_avg = m(x_avg) + b

8.48333 = -1.3(1.1666) + b

b = 9.9989

y = -1.3x + 10

The slope of given data is a -3.

According to the statement

we have given a some data and we have to find the slope of the data.

So, data given is:

x, has the entries, negative 2, negative 1, 0, 1, 2.

y, has the entries, negative 2, 1, 4, 7, 10.

and we have to find the slope of the data

So, we know that it is a data represent in the graph then

We know that a there is a graphical representation of data.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

And when we observe this data then we see that the there is some increase the y axis value as compare to the x axis values.

So,

For each unit of run in the x-values, there is an increase of 3 in the y-values. The slope is rising over Run so 3/1 = 3

So, The slope of given data is a -3.

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Answer: the answer is a -3

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

That would be 4/15 * 360   as there are 360 degrees in a circle

= 96 degrees.

Answer:

4. b) an angle

5. b) the angles of a triangle

6. b) opposite, hypotenuse and adjacent

Step-by-step explanation:

4. To find sine, cosine, tangent, you use the sin, cos, tan key of the calculator.

If you are given the value of the sin, cos, tan, and you are looking for the angle, then you use the second function of the calculator.

Answer: b) angle

5. angles of a triangle

6. The sides that form the right angle are the legs. In trig, there is an angle of interest, so to distinguish between the legs, one leg is called the adjacent leg, and the other leg is called the opposite leg. The side opposite the right angle is the hypotenuse.

Answer: opposite, hypotenuse and adjacent

Answer:

Step-by-step explanation:

9,328 and you would divide that by 98 and the answer would be 95.18367347 boxes

i) The number of students that come to school by motorcycle only = 8

ii) The number of students that did not take all the three types of transportation = 9

iii) Number of students that did not come to school by car = 28

The total number of students = 40

The number of students that come to school by car alone = 9

The number of students that come to school by motorcycle only = 8

The number of students that come to school by car only = 11

The number of students that come to school by both car and motorcycle = 3

Number of students that did not take all the three types of transportation = 40 - (9 + 8 + 3 + 11)

= 40 - 31

Number of students that did not take all the three types of transportation = 9

Total students that come to school by car = 9+3 = 12

The total number of students that did not come to school by car = 40 - 12 = 28

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Answer:

$96

Step-by-step explanation:

The total weight of the package was 20 pounds, given the total shipping cost was $3.45, using the total cost function, C(P) = 1.65 + 0.12(P - 5), where P is the weight of the package in pounds.

In the question, we are given that a package weighs P pounds, P being a whole number. To ship this package by express costs $1.65 for the first five pounds and 12c for each additional pound. The total shipping cost was $3.45.

We are asked for the package weight in pounds.

First, we design a general cost function.

The cost is given to be $1.65 for the first 5 pounds, and 12c for each additional pound.

The weight of the package is given to be P pounds.

We assume the total cost function to be C(P), a function of the weight of the package, P pounds.

Thus, the total cost function can be shown as the sum of $1.65 and 12c or $0.12 multiplied with (P - 5), as it is the cost for additional pounds after 5 pounds.

Thus, the total cost function, C(P) = 1.65 + 0.12(P - 5).

Now, we are given that the total shipping cost was $3.45.

Thus, to find the weight of the package, we equate the total cost function, C(P) to 3.45, to get:

1.65 + 0.12(P - 5) = 3.45,

or, 1.65 + 0.12P - 0.6 = 3.45,

or, 0.12P + 1.05 = 3.45,

or, 0.12P = 3.45 - 1.05,

or, 0.12P = 2.40,

or, P = 2.40/0.12 = 20.

Thus, the total weight of the package was 20 pounds, given the total shipping cost was $3.45, using the total cost function, C(P) = 1.65 + 0.12(P - 5), where P is the weight of the package in pounds.

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Answer:

x = 5, y = sqrt6, z = 3

Step-by-step explanation:

[tex]\frac{10}{\sqrt{6} } \\\\\frac{(10)(\sqrt{6} )}{(\sqrt{6} )(\sqrt{6}) } \\\\\frac{10\sqrt{6} }{6} \\\\or\\\\\frac{5\sqrt{6} }{3}[/tex]

❄ Hi there,

let us revise the way we rationalize the denominator before we get down to the actual process.

__________

Suppose you had a problem, and you did all the steps, and you arrived at the following answer: [tex]\sf{\dfrac{10}{\sqrt6}}[/tex].

Well, this answer is not in its simplest form, because it has an irrational number in its denominator.

So what we do is we get rid of that irrational number in the denominator  by multiplying the fraction's top & bottom by [tex]\sqrt6[/tex]:

[tex]\sf{\dfrac{10\sqrt6}{\sqrt6\times \sqrt6}}[/tex]

Now we simplify

[tex]\sf{\dfrac{10\sqrt6}{6}}[/tex]

Reduce

[tex]\sf{\dfrac{5\sqrt6}{3}}[/tex]

- - - - -  - - -

Answer:

(12,1)

Step-by-step explanation:

We know that ordered pairs are in the format of (x,y).

This means in that (12, __) 12 is our x coordinate. Plugging 12 into the equation as x we get:

[tex]12-3y=9\\-3y=9-12\\-3y=-3\\y=1[/tex]

Therefore our answer is (12,1) as we plug y back into our coordinate (x,y).

Answer:

(12,1)

Step-by-step explanation:

In the ordered pair, x=12

plug 12 back in the equation

12-3y=9

-3y=-3

3y=3

y=1

The value of p(cc and tc) is 0.1173

The distribution of the replies is 0.12, as shown by the two-way table.

We've done that.

520 randomly chosen individuals from the teen, young adult, and adult age groups were asked about their preferred musical genres by the researcher.

The distribution of the answers is shown in the two-way table.

There are 61 teenagers in the country.

seeing as how this is only one of 520,

The probability formula?

P(E) = (Number of favorable outcomes) = Probability of an Event (Sample space).

61/520=0.1173

We calculate 0.1173 by dividing 61 by 520 and rounding to the next hundredth to obtain 0.12.

Thus the value of p(cc and tc) is 0.1173.

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Answer:

Step-by-step explanation:

Well first you have:

$15.95 for one sweater
$9.00 each for two shirts

You would double the amount $9.00 which would be:

9 + 9 = 18 or Multiply 9 x 2 = 18

So this would total to 15 + 18 = $33

The coefficient of t to the 4th power in the given expansion is -167403915.

Option (c) is the correct answer.

An expansion of a product of sums uses the fact that multiplication distributes across addition to represent it as a sum of products. A polynomial expression can be expanded by repeatedly substituting equivalent sum of products for subexpressions that multiply two other subexpressions, at least one of which is an addition, up until the expression becomes a sum of (repeated) products. Simplifications like grouping similar terms or canceling terms may also be used during the expansion.

Given expansion=[tex](-9t-9)^{7}[/tex]

Coefficient of the 4th power of t in the expansion,

=[tex]_{7} {C} _{7-4} (-9t)^{4}(-9)^{7-4}[/tex]

=[tex]_{7}C_{3}(-9)^{4}t^{4}(-9)^{3}[/tex]

=[tex]_{7}C_{3}(-9)^{7}t^{4}[/tex]

=[tex]35t^{4}(-9)^{7} \\[/tex]

=[tex]35t^{4}(4782969)[/tex]

= -167403915[tex]t^{4}[/tex]

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Answer:

C) 6

Step-by-step explanation:

3 garden rows = 3*5 = 15 feet

we know we need 2 packages per each 15 feet

45/15=3 so 3 15 in 45, we just multiply 3 and 2 to get 6 packages

An absolute value inequality for "all numbers less than 7 and greater than -7" is given by |x| < 7.

Based on the information provided, we can logically deduce that the statement describes an intersection of set because the word "and" was used.

This ultimately implies that, we would use the less than (<) symbol to write an absolute value inequality for the given statement:

|x| < 7

Therefore, this can be translated as follows:

-7 < x < 7      or      x < 7  and    x > -7.

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The maximum height of the ball that is displayed by the graph is: D. 108 feet.

A graph is a statistical diagram that displays the relation between two variables. One of the variables is plotted on the x-axis (horizontal axis) against the other variable on the y-axis (vertical axis).

The variable on the x-axis (horizontal axis) is the input, while the variable on the y-axis (vertical axis) is the output.

Considering the given graph in the image above, we have the following variables:

On the x-axis (horizontal axis): time which is the input

On the y-axis (vertical axis): height of the ball which is the output.

Thus, the peak of the line represents the maximum height the ball reaches. The maximum height which is the peak is approximately 109 feet.

Therefore, the maximum height is: D. 109 feet.

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Answer:

109 feet

Step-by-step explanation:

just took the lesson

The volume of wedge is 4/15 by use of Triple integral.

According to the statement

we  have to find the volume of wedge which is bounded by the parabolic cylinder.

So, because of the given shape of z=√y

the plane y=0 is a boundary, in addition to the given x = 0, z = 0.

so we are in the first octant for all of this. and the further constraint is the plane x + y = 1

Triple integrals are 3 successive integrations, used to calculate a volume, or to integrate in a 4th dimension, over 3 other independent dimensions.

but as a triple integral you would write:

∫x=0 ∫y=0∫z=0 dz dy dx

And after put the values in it and solving it we get the

[−4/15(1−x)^5/2] at x=0

Then after that the answer will become 4/15.

So, The volume of wedge is 4/15 by use of Triple integral.

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The coordinates of the vertices are (-1, 6), (1, 2) and (2, 3)

The functions are given as:

y = x + 1

2x + y = 4

x + y = 5

Next, we plot the graph of the lines (see attachment)

From the attached graph, the coordinates of the vertices are (-1, 6), (1, 2) and (2, 3)

Rewrite the equations in slope intercept form

y = x + 1 ⇒ Slope = 1

y = -2x + 4 ⇒ Slope = -2

y = -x + 5 ⇒ Slope = -1

The equations y = x + 1 and y = -x + 5 have their slopes to be opposite reciprocals

This means that the lines are perpendicular (they form a right angle)

Hence, the triangle is a right triangle

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The triangles are similar by SAS principle.

Similar triangles have the same shape but may have different sizes.

In similar triangles, corresponding sides are always in the same ratio.

The corresponding angles are congruent.

Therefore, using SAS ratio,

6 / 8 = 8 × 3 / 32

6 / 8  = 24 / 32 = 3 / 4

Therefore, the corresponding sides are a ratio of each other.

Therefore, the triangles are similar by SAS principles because the two triangles have two pairs of sides in the same ratio and the included angles are also equal

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In the given figure of circle, if RT = 90, SU = 25, and SO is perpendicular to RT, the length of the radius RO is 53.

In the given figure,

RT = 90

SU = 25

SO is perpendicular to RT.

Here, SO and RO are the radii of the circle and RT is a chord.

The length of the chord, RT is given as,

RT = 2 √(r² - d²)

Here, r is the radius and d is the distance of the chord RT from the center O.

Radius, r = RO and distance, d = OU

∴ RT = 2 √(RO² - OU²)

Substituting RT = 90 in the above equation, we get,

90 = 2 √[(RO)² - (OU)²]

√[RO)² - (OU)²]  = 45

(RO)² - (OU)² = 45²

(RO)² - (OU)² = 2025 ........... (1)

Now, OU = SO - SU   [From the figure]

⇒ OU = SO - 25

Substituting OU = SO - 25 in equation (1), we obtain,

(RO)² - (SO - 25)² = 2025

(RO)²- [(SO)² + (25)² - 2(SO)(25)] = 2025    [ ∵ (a-b)² = a²+b²-2ab ]

(RO)²- (SO)² - (25)² + 50(SO) = 2025 ........... (2)

Since, RO and SO both are the radii of the same circle, we have,

SO = RO

Thus, we can write equation (2), as follows,

⇒ (RO)² - (RO)² - (25)² + 50(RO) = 2025

⇒ -625 + 50RO = 2025

⇒ 50RO = 2025 + 625

⇒ RO = 2650/50

⇒ RO = 53

Hence, the length of the radius RO of the given circle is 53.

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From the conversation it can be inferred that Paul's approach to getting on the horse is methodical (option c).

A methodical attitude or behavior refers to the preference of people to use an organized method and sequences to perform an activity correctly.

According to the above, it can be inferred that Paul behaves in a methodical manner because he prefers to relate to the horse slowly and in a controlled manner before proceeding to mount it.

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