Ms. Reynolds is asking students to find
the volume of the rectangular pyramid
below. Which student wrote the
correct expression for the value of B,
the area of the base ?

Peter: 5•13

Thelma: 1/3 (13•12)

Answer:

200

Step-by-step explanation:

0.2 * x = 40

40 / 0.2 = 200

The equivalent logarithmic statement is log base 3 of 9 = 2 for the equation 9 = 3².

To convert the exponential statement 9 = 3² into an equivalent logarithmic statement, we can use the logarithm with base 3.

Step 1: Identify the base and exponent in the exponential statement.

In our case, the base is 3 and the exponent is 2.

Step 2: Write the equivalent logarithmic statement.

Using the base 3 logarithm, we have:

log₃(9) = 2

This logarithmic statement can be read as "the logarithm base 3 of 9 is equal to 2."

The logarithm function gives us the exponent or power that the base needs to be raised to in order to obtain the given number. In this case, log₃(9) tells us that 3 raised to the power of 2 equals 9.

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Answer:

0.004 km; 400 cm; 4000 mm

Step-by-step explanation:

1 km = 1000 m

1 = (1 km)/(1000 m)

4 m * (1 km)/(1000 m) = 4/1000 km = 0.004 km

1 m = 100 cm

1 = (100 cm)/(1 m)

4 m * (100 cm)/(1 m) = 400 cm

1 m = 1000 mm

1 = (1000 mm)/(1 m)

4 m * (1000 mm)/(1 m) = 4000 mm

Answer: 0.004 km; 400 cm; 4000 mm

Answer:

The other base measure 18.76 yd.

Step-by-step explanation:

A = h ((a+b) / 2)

213.86 = 18 ((5 + b) /2)

(5 + b) /2 = 11.88

5 + b = 23.76

b = 18.76 yd

The coordinates satisfy the equation x^2 + y^2 = 1. In this specific problem, we found that P(x, y) = (3 * sqrt(10)) / 10 , - (sqrt(10)) / 10.

To solve this problem, we need to recall some basic trigonometry concepts related to the unit circle. The unit circle is a circle of radius 1 centered at the origin of a coordinate plane. Any point on the unit circle can be represented by its coordinates (x, y), where x and y are the horizontal and vertical distances from the origin, respectively.

Since the given problem tells us that the x-coordinate of P is positive, we know that x > 0. Additionally, we are given that the y-coordinate of P is -(square root 10)/10. We can use this information to solve for x.

From the Pythagorean theorem, we know that for any point (x, y) on the unit circle, x^2 + y^2 = 1. Substituting y = -(square root 10)/10, we get:

x^2 + ((-sqrt(10))/10)^2 = 1

Simplifying this expression, we get:

x^2 + 10/100 = 1

x^2 = 90/100

x = sqrt(90)/10

Since we know that x is positive, we can simplify this expression further by factoring out a square root:

x = (sqrt(9) * sqrt(10)) / 10

x = (3 * sqrt(10)) / 10

Therefore, the coordinates of point P are:

P(x, y) = (3 * sqrt(10)) / 10 , - (sqrt(10)) / 10

We can check our answer by verifying that these coordinates satisfy the equation x^2 + y^2 = 1:

(3 * sqrt(10) / 10)^2 + (-sqrt(10) / 10)^2 = 9/100 + 10/100 = 1/10

Simplifying this expression, we get:

1/10 = 1/10

This confirms that our answer is correct and that P lies on the unit circle.

In summary, to find the coordinates of a point P on the unit circle given its y-coordinate and the fact that its x-coordinate is positive, we can use the Pythagorean theorem to solve for the x-coordinate. We then check our answer by verifying that the coordinates satisfy the equation x^2 + y^2 = 1. In this specific problem, we found that P(x, y) = (3 * sqrt(10)) / 10 , - (sqrt(10)) / 10.

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To evaluate the triple integral ∫∫∫ xyzdv using cylindrical coordinates, we need to express the integral in terms of the cylindrical coordinates (ρ, φ, z).

The given solid E lies under the paraboloid z = 4 - z² - y². In cylindrical coordinates, this paraboloid equation becomes z = 4 - ρ² - y².

To set up the triple integral, we need to determine the limits of integration for each variable.

Since the solid lies in the first octant, the limits of integration are as follows:

ρ: from 0 to some value ρ₁

φ: from 0 to π/2

z: from 0 to the upper limit of the paraboloid, which is given by the equation z = 4 - ρ² - y².

Now we can set up the triple integral:

∫∫∫ xyzdv = ∫₀^(π/2) ∫₀^ρ₁ ∫₀^(4-ρ²-y²) (ρcosφ)(ρsinφ)z dz dρ dφ

Simplifying the integrand and integrating, we can evaluate the triple integral to obtain the final result.

Note: The specific value of ρ₁ and the complexity of the integration depend on the precise shape of the solid E, which is not provided in the given information. Therefore, the final evaluation of the integral requires additional information about the solid E.

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A = $5,800.00

I = A - P = $1,800.00

hey!

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 15%/100 = 0.15 per year.

Solving our equation:

A = 4000(1 + (0.15 × 3)) = 5800

A = $5,800.00

The total amount accrued, principal plus interest, from simple interest on a principal of $4,000.00 at a rate of 15% per year for 3 years is $5,800.00.

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hope i helped in some way..have great day!

Answer:

5/6?

Step-by-step explanation:

Answer:

The exterior angle is 35° + 62° = 97°

And 97° > 35°

And 97° > 62°

Step-by-step explanation:

Answer:

pppop-

That’s what u get

Step-by-step explanation:

a) The relation is reflexive, symmetric, and transitive.

b) The relation is not reflexive, symmetric, or transitive.

a) For each watermelon x, x is related to x because the measured weight of x is at least the measured weight of x. Therefore, the relation is reflexive.

For each watermelon x and y, if x is related to y (meaning the measured weight of x is at least the measured weight of y), then y is also related to x (meaning the measured weight of y is at least the measured weight of x). Therefore, the relation is symmetric.

For each watermelon x, y, and z, if x is related to y (meaning the measured weight of x is at least the measured weight of y) and y is related to z (meaning the measured weight of y is at least the measured weight of z), then x is related to z (meaning the measured weight of x is at least the measured weight of z). Therefore, the relation is transitive.

b) For each watermelon x, x is not related to x because no two watermelons have the same measured weight. Therefore, the relation is not reflexive.

For each watermelon x and y, if x is related to y (meaning the measured weight of x is at least the measured weight of y), then y is not related to x (meaning the measured weight of y is not at least the measured weight of x).

Therefore, the relation is not symmetric. For each watermelon x, y, and z, if x is related to y (meaning the measured weight of x is at least the measured weight of y) and y is related to z (meaning the measured weight of y is at least the measured weight of z), then x is not related to z (meaning the measured weight of x is not at least the measured weight of z).

Therefore, the relation is not transitive.

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Answer:30.7 mybe i am not 100%

Step-by-step explanation:first you would devide 40 by 4 and then you would round

Answer:

If you begin with the graph for f(x) and then substituted x+3 for x, the effect on the graph will be to move the whole graph 3 units to the left.  

Given that (-9,-1) is on the graph of f(x), and that we are to move the entire graph 3 units to the left, then the coordinate -9 becomes -9-3, or -12:  (-12,-1).

Step-by-step explanation:

Brand X needs to use 8.4 oz. of Brand A mixed nuts and 12.6 oz. of Brand B mixed nuts to achieve a 29% peanut content in their 21 oz. bags of mixed nuts.

To determine how much of Brand A and Brand B mixed nuts Brand X needs to use to achieve a 29% peanut content in their 21 oz. bags of mixed nuts, we can set up an equation based on the principle of weighted averages.

Let's assume x represents the amount of Brand A mixed nuts (35% peanuts) that Brand X needs to use, and y represents the amount of Brand B mixed nuts (25% peanuts) that Brand X needs to use.

The total weight of the mixed nuts is given as 21 oz., so we can set up the following equation:

x + y = 21 (Equation 1)

To achieve a 29% peanut content in the final product, we can set up another equation based on the peanut content:

(35% of x) + (25% of y) = 29% of 21 oz.

0.35x + 0.25y = 0.29 * 21 (Equation 2)

Now we have a system of two equations (Equation 1 and Equation 2). We can solve this system of equations to find the values of x and y.

Let's solve the system using the substitution method:

From Equation 1, we have: x = 21 - y

Substituting this into Equation 2, we get:

0.35(21 - y) + 0.25y = 0.29 × 21

7.35 - 0.35y + 0.25y = 6.09

0.1y = 6.09 - 7.35

0.1y = -1.26

y = -1.26 / 0.1

y = 12.6

Substituting this value back into Equation 1, we can find x:

x + 12.6 = 21

x = 21 - 12.6

x = 8.4

Therefore, Brand X needs to use 8.4 oz. of Brand A mixed nuts and 12.6 oz. of Brand B mixed nuts to achieve a 29% peanut content in their 21 oz. bags of mixed nuts.

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The relationship between the variables x and y, based on the given data points, can be represented by the equation y = -3.30x + 9.77.

This linear equation captures the trend observed in the data, providing a mathematical expression to estimate the value of y corresponding to a given x. By performing linear regression on the provided data points, the equation y = -3.30x + 9.77 is derived. This equation represents a linear relationship between x and y, where the coefficient of x is -3.30, indicating that as x increases, y decreases at a rate of 3.30 units.

The constant term 9.77 represents the y-intercept, which is the value of y when x is 0. This equation serves as a model to estimate the value of y for any given x within the observed range. It provides a straightforward and concise representation of the relationship between the variables based on the given data.

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Answer:

The third one down

Step-by-step explanation:

Answer:

10 flags

Step-by-step explanation:

7.42/0.7

Round down since you cant "round up" when talking about physical objects.

Answer:

10 Flags

Step-by-step explanation:

The Hindu Arabic numeral for the Mayan numeral is 103.

The given Mayan numeral needs to be converted to Hindu Arabic numeral.

The Hindu Arabic numeral system includes ten digits from 0 to 9. This numeral system is used to represent numbers in almost all the countries in the world.

10:03 in Mayan Numeral System is as shown below:MAYAN_NUMERALS:    10:03 = 10.|. 0. | 3. ||||||. |||..........||||||... ||.......... |||||||||||||||||||||||||||||||10.|.0.|.3.|.    =   103The above given Mayan Numeral system converted to Hindu Arabic Numeral is 103.

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Answer:

30 degrees

all triangles equal 180 degrees

90+60=150

180-150=30

Step-by-step explanation:

Answer:A

Step-by-step explanation:

the y-intercept is when x-axis is 0 and that means that hours of jogging is 0 and the y-axis is 1 minunte

Answer:

The first option.

Step-by-step explanation:

The y-intercept is where the line crosses through the y-axis, which, in this case, would be at point (0, 1). The labeling on the left side shows what each number on the y-axis represents, and it would be minutes stretching when not jogging.

hope this helped! :)

Serena started with approximately $173.33 money.

Let's denote the initial amount of money Serena had as S and the initial amount of money Visala had as V.

According to the problem, their combined total was $180, so we have the equation S + V = 180.

After Serena gave Visala $20, Serena's remaining amount became S - 20, and Visala's amount became V + 20.

Visala then gave Serena a quarter of the money she had, which is (V + 20)/4. After this transaction, Serena's total amount became S - 20 + (V + 20)/4, and Visala's total amount became V + 20 - (V + 20)/4.

It is given that after these transactions, they each had the same amount. Therefore, we can set up the equation:

S - 20 + (V + 20)/4 = V + 20 - (V + 20)/4.

Let's simplify and solve for S:

4S - 80 + V + 20 = 4V + 80 - V - 20.

Combining like terms:

4S + V = 3V + 160.

Substituting the value of S + V = 180 from the first equation:

4S + V = 3(180) + 160,

4S + V = 540 + 160,

4S + V = 700.

Now, we have two equations:

S + V = 180,

4S + V = 700.

Subtracting the first equation from the second equation:

4S + V - (S + V) = 700 - 180,

3S = 520,

S = 520/3 ≈ 173.33.

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There is a 99.73% chance that two people selected at random will not share the same birthday out of 365.

The probability of two people not sharing the same birthday out of 365 can be calculated using the formula:P(A) = n(A)/n(S)where n(A) is the number of favorable outcomes and n(S) is the total number of possible outcomes.

In this case, the favorable outcome is that two people do not share the same birthday, and the total number of possible outcomes is 365 × 365 since each person can have a birthday on any of the 365 days.

To find the number of favorable outcomes, we need to subtract the number of ways two people can have the same birthday from the total number of possible outcomes.

The number of ways two people can have the same birthday is simply 365 since there are 365 possible birthdays.

Therefore, the number of favorable outcomes is:365 × 364

The total number of possible outcomes is:

365 × 365

Thus,the probability of two people not sharing the same birthday out of 365 is:P(A) = (365 × 364)/(365 × 365)P(A) ≈ 0.9973

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Answer:

68

Step-by-step explanation:

Answer: 5^2 + 4^3 - 21= 68

Answer:

See, this is what i do not get. equations like this. People now in days would just by faster internet speed. Why would we need to know this if  we will never ever get to use this in our life. Also you could just call the internet cable person. This makes absolutely no since at all. Also who even uses Netflix anymore?

Step-by-step explanation

Answer:

3 times greater

Step-by-step explanation:

6.7 x 10 to the 6 = 6700000

2x 10 to the 7 = 20000000

20000000/6700000 = 2.98507462687

Rounded - 3

Answer:

[tex] \: x = 10[/tex]

Step-by-step explanation:

prefer the attachment

according to the question

[tex] \displaystyle \: \frac{6}{17.5-x} = \frac{8 + 6}{17.5} [/tex]

simplify addition:

[tex] \displaystyle \: \frac{6}{17.5-x} = \frac{14}{17.5 } [/tex]

simplify fraction;

[tex] \displaystyle \: \frac{6}{17.5 - x} = 0.8[/tex]

cross multiplication:

[tex]\displaystyle 6 = 14 - 0.8x[/tex]

cancel 14 from both sides:

[tex] \displaystyle - 8= - 0.8x[/tex]

divide both sides by -0.8:

[tex] \therefore \: x = 10[/tex]

31 additional days, getting behind by 31 seconds; this, added to the original 4 sec behind, gives you a total 35 seconds behind.

Now, that really isn't complicated, right?

Answer:

158

Step-by-step explanation:

All i know is that these answer choices cannot be found in the calculator

Answer:

158.....

PEMDAS

you multiply first 6+160-8

then you add or subtract

158