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complete the statement

1. Volume of pyramid= ________× volume of rectangular prism, V= l×w×h
So for pyramid, V= 1/3 (l×w×h) = (l×w×h) ÷ ________.

2. The volume of the cylinder is three times the volume of the cone or the volume of the is _________ that of the cylinder.

3. Volume of the cone = ________ volume of the cylinder.
4. Sphere's volume is 2/3 of the _________ volume.

please answer this questions because this is need to pass tomorrow!!​

The possible values for t for the points A and B with gradient 2 are t = -1 or t = 3/2.

Given the gradient 2 for the point A and B, we have that;

gradient = (y₂ - y₁)/(x₂ - x₁)

so;

2 = (2t² + 7 - t)/(7 - 2)

2 = (2t² + 7 - t)/5

10 = 2t² + 7 - t {cross multiplication}

2t² + 7 - t - 10 = 0

2t² - t - 3 = 0

2t² + 2t - 3t - 3 = 0 {we rewrite the middle term}

2t(t + 1) -3(t + 1) = 0

(2t - 3)(t + 1) = 0 {factorization}

2t - 3 = 0 or t + 1 = 0

t = 3/2 or t = -1

Therefore, the possible values for t for the points A and B with gradient 2 are t = -1 or t = 3/2.

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Answer:

(1.5, 0.5)

Step-by-step explanation:

(5, 3) and (-2, -2)

5 - 2 / 2 = 1.5

-2 + 3 / 2 = 0.5

Answer:

42 folds. This fact is mentioned in search results [1], [2], [3], [4], [5], and [7]. It is also noted in search result [6] that the answer may be 45 folds instead of 42, but this is in the context of a discussion on exponential growth and is not a commonly accepted answer to the question. Finally, search result [10] poses a similar question but provides the same answer of 42 folds to reach the moon.

Step-by-step explanation:

Earth's diameter is 0.0092 times less than the sun's diameter.

The Diameter of Earth = 1.3 * 10⁴ km

The Diameter of Moon = 3.5 * 10³ km

Let the diameter of sun be x km

According to the question

The diameter of the sun is 400 times that of the moon.

x = 400 * 3.5 * 10³ km

= 14 * 10⁵ km

The Diameter of earth / diameter of sun

=  1.3 * 10⁴ / 14 * 10⁵

= 0.0092

Hence, The diameter of the Earth is 0.0092 times that of the Sun.

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The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

According the question,

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

Where x represents the quantity of additional tours that the tourist wants to add to their travel package.

The function f(x) represents the total cost of the travel package plus the additional cost of the extra tours.

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Answer:

she bought 5 shakes

Step-by-step explanation:

shakes: $3.39

tea: $2.50

2.50 + 3.39s = 19.45

3.39s = 16.95

s = 16.95 ÷ 3.39

s = 5

Check:

2.50 + 3.39(5) = 19.45

or

2.50 + 3.39 + 3.39 + 3.39 + 3.39 + 3.39 =  19.45

The expression of the given statement is 2y - 3  = -1

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. The operations of mathematics include multiplication, division, addition, and subtraction.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Let's look at how expressions are written.

The expression of the given statement is 2y - 3  = 4.

Here, let the unknown number = y

Now, product of y and 2 =  2 times  y   =   2y

Also, three less than the product   =  Product - 3

So, three less than the product  of 3 and y =  2 y - 3

Now, this above expression is equivalent to -1.

⇒2 y - 3  = -1

Hence the expression of the given statement is 2y - 3  = -1

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The sentence "Three less than the product of 2 and a number is 4" can be translated into the equation: 2x - 3 = 4

A mathematical statement that demonstrates the equivalence of two expressions is known as an equation.

It has two sides that are divided by the equals sign (=).

Variables, constants, coefficients, operators, and functions can all be used in the expressions on either side of the equation.

Here, x represents the unknown number that we are trying to solve for. The expression "the product of 2 and a number" is represented by 2x, and "three less than" is represented by the subtraction of 3 from that product. This expression is set equal to 4, which is the result given in the original sentence.

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Answer: 2662.25 (now u just need to round it to the whole)

Step-by-step explanation: Ok we know that it can last 5750 years, and we know 53.7 percent of those years is gone, meaning it only got 46.3 percent of it years left. until it gone. So 46.3 percent of 5750 is 2662.25. Now go round it if u need to.

\(\\ \sf\longmapsto -15-|15-|-15||\)

\(\\ \sf\longmapsto -15-|15-15|\)

\(\\ \sf\longmapsto -15-|0|\)

\(\\ \sf\longmapsto -15-0\)

\(\\ \sf\longmapsto -15\)

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\( \sf \: -15- \left| 15- \right| -15 \left| \right|\)

The absolute value of a real number 'a' is 'a' when \(\sf\:a\geq 0\), or '-a' when a < 0. The absolute value of -15 is 15.

\( \sf \: -15-|15-15| \)

Subtract 15 from 15 to get 0.

\( \sf \: -15-|0| \)

The absolute value of a real number 'a' is 'a' when \(\sf\:a\geq 0\), or '-a' when a < 0. The absolute value of 0 is 0.

\( \sf \: -15-0 \)

Subtract 0 from -15 to get -15.

\( \boxed{ \boxed{ \bf \: -15 }}\)

Answer: I THINK 250

Step-by-step explanation: 125 is half and 125 times 2 is 250.

Answer:

-5.1

Step-by-step explanation:

Since we know the starting temperature was -12.6 and the decrease was 7.5, that gives an equation.

-12.6 - 7.5.

Since we are working in temperature we need to be careful when subtracting.

-12.6 - 7.5 = -5.1

In a calculator, -12.6 - 7.5 would be 20.1 but since we are using temperature the answer is -5.1.

Hope that helps. x

Based on the data in the sample, we can estimate that 900 people in attendance would prefer mustard on a hot dog.

According to the data provided, out of the 150 people surveyed, 27 people prefer mustard on a hot dog.

To estimate how many people in attendance would prefer mustard on a hot dog, we can use a proportion:

27/150 = x/5000

Where x is the number of people in attendance who would prefer mustard on a hot dog.

To solve for x, we can cross-multiply:

27 x 5000 = 150 x

Simplifying the equation, we get:

x = (27 x 5000)/150

x = 900

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The three types of expressions that can be written by exponents are

2³ × 3³;   2. 6¹ × 6² and 6 × 2² × 3².

Exponents are mathematical notations used to represent the repeated multiplication of a number by itself.

An exponent is a small number written above and to the right of a base number, which indicates the power to which the base is raised.

For example, in the expression 2³, 2 is the base number and 3 is the exponent.

Here we have 6 to the third power = 216.  

=> 6³ = 216

Here are three more expressions whose value is 216 using exponents:

1.  2³ × 3³

Explanation:  2³ = 8 and  3³ = 27 , so  2³  × 3³ = 8 × 27 = 216

2.  6¹  ×  6²

Explanation:  6¹ = 6  and 6² = 36, so  6¹  × 6² = 6 × 36 = 216

3.  6 × 2² × 3²

Explanation:  2² =  4 and  3² = 9 so 4 × 9 × 6 = 216  

Therefore,

The three types of expressions that can be written by exponents are

2³ × 3³;   2. 6¹ × 6² and 6 × 2² × 3².

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Given:

The IQ of 10 randomly selected senior high school students are given as:

102,125,120,128,116,108,124,115,109,99.

Required:

To compute the sample mean, variance and standard deviation. ​

Explanation:

First, we will calculate the sample mean .

Here, the IQ of 10 students is given.

Therefore, total number of students (n) = 10.

Thus,

Next, the variance is given as follows:

Now, we have,

Thus,

Next, the standard deviation is,

Final Answer:

The mean is 114.6.

The variance is 98.27.

The standard deviation is 9.9131.

Using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place.

Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Simply put, probability is the likelihood that something will occur.

When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes.

So, we have the chart:

Penny = 2/5 = 0.4

Nickel = 1/5 = 0.2

Dime = 1/4 = 0.25

Then, the probability of getting a value of at least $0.10

P(E) = 3/3

P(E) = 1

Therefore, using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

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The value of the expression when k = 9 is 399

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

5k^2 − 6

When the value of k is

k = 9

We have, the following equation

5k^2 − 6 = 5(9)^2 − 6

Evaluate the exponent

5k^2 − 6 = 5 * 81  − 6

Evaluate the product

5k^2 − 6 = 405  − 6

Evaluate the difference

5k^2 − 6 = 399

Hence, the value of the expression when k = 9 is 399

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Answer:

A' is (-1,-1) B' becomes (-1,-4) C' becomes (-3,-1)

Step-by-step explanation:

To take a shortcut, reflecting a figure across both axes is the same as rotating a figure 180 degrees about the orgin using formula x,y goes to -x,-y but to explain it. Use formula (x,y) goes to (x,-y) to reflect it across x-axis then use formula (x,y) goes to (-x,y) to reflect it across y-axis. A' becomes -1,-1. B' becomes -1,-4 . C' becomes (-3,-1)

The surface area of the triangular prism would be =324,000cm²

To calculate the surface area of the triangular prism the formula that should be given would be as follows:

Surface area of triangular prism;

Surface area of triangular prism;= bh+(b1+b2+b3)l

where:

base length = 20cm

height = 15cm

length = 18cm

SA = 20×15(20+15+25)×18

= 300×60×18

= 324,000cm²

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Answer:

Step-by-step explanation:

From the given information:

ΔG° = -30.5 kJ/mol

By applying the following equation to calculate the value of K.

ΔG° =-RT㏑K

making ㏑ K  the subject of the formula:

\(\mathtt{ In \ K} = \dfrac{\Delta G^0}{-RT}\)

where;

Temperature at 25° C = (25 + 273)K

= 298K

R = 8.3145 J/mol.K (gas cosntant)

\(\mathtt{ In \ K} = \dfrac{-30.5 \times 10^{3}\ J /mol} {-(8.3145 \ J/mol. K \times 298 \ K}\)

\(\mathtt{ In \ K} = \dfrac{-30.5 \times 10^{3}\ J /mol} {-2477.721 J/mol }\)

㏑K = 12.309

\(K = e^{12.309}\)

K = 221682.17

K = 2.22 × 10⁵

b) The reaction for the metabolism of glucose is given as:

\(C_6H_{12} O_6 + 6O_{2(g)} \to + 6CO_{2(g)} + 6H_2O_{(l)}\)

From the above expression, let calculate the Gibbs free energy by using the formula:

\(\Delta G^0_{rx n }= \Delta G^0_{product}- \Delta G^0_{reactant}\)

\(\Delta G^0_{rx n }= [6 \times \Delta G^0_{f}(CO_2) + 6 \times \Delta G^0_{f}(H_2O)] - [1 \times \Delta G^0_{f}(C_6H_{12}O_6) + 6 \times \Delta G^0_{f}(O_2)]\)

At standard conditions;

The values of corresponding compounds are substituted into the equation above:

Thus,

\(\Delta G^0_{rx n }= [6 \times (-394) + 6 \times (-237)] - [1 \times (-911) + 6 \times (0)] \ kJ/mol\)

\(\Delta G^0_{rx n }= [-2364-1422] - [-911+0] \ kJ/mol\)

\(\Delta G^0_{rx n }= -3786 +911 \ kJ/mol\)

\(\Delta G^0_{rx n }= -2875 \ kJ/mol\)

\(\Delta G^0_{rx n }= -2875000 \ J/mol\)

Now, the no of ATP molecules generated = \(\dfrac{\Delta G^0 \text{of metabolism for glucose}}{\Delta G^0 \text{of hydrolysis for ATP}}\)

= (-2875000 J/mol ) / -30500 J/mol

= 94.26

≅ 94 ATP molecules generated

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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Answer:

x = 32 words

Step-by-step explanation:

Okay...let's get solving! :D Firstly, we

let the word list be x and convert the long paragraph into an equation that we can use.

one-fourth = 1/4

Memroized = 8 words

\(x * \frac{1}{4} = 8\)

Thus, we solve the equation.

x = 32 words

The rectangle has a length of 8 units along the top and bottom sides, and a height of 6 units along the vertical sides.

A rectangle is a four-sided flat shape with four right angles (90 degree angles) between the sides. It is a type of quadrilateral, which means a shape with four sides.

To find the length of the sides of the rectangle, we can use the distance formula:

d = √((x2 - x1)²+ (y2 - y1)²)

Using the coordinates (-4,4) and (4,4) for the two endpoints of the top side of the rectangle, we get:

d = √((4 - (-4))² + (4 - 4)²) = 8

Since the top side has length 8 and there are two top and two bottom sides of equal length, the perimeter is:

20 = 28 + 2L

where L is the length of one of the vertical sides. Solving for L, we get:

L = (20 - 2*8)/2 = 2

Therefore, the length of the vertical sides of the rectangle is 2 units.

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The length of rectangle is 8 units on the x-axis, and the width of rectangle is 4 units along the y-axis.

The whole distance encircling a rectangle's edge is known as its perimeter. It is the total of the measurements of the rectangle's four sides.

The formula for calculating the perimeter P of a rectangle with length L and width W is as follows:

P = 2L + 2W

According to question:

To find the length of the sides of the rectangle, we can use the distance formula:

\(d = \sqrt{((x_{2} - x_{1} )^2+ (y_{2} - y_{1})^2)}\)

Using the coordinates (-4, 4) and (4, 4)

\(d = \sqrt{((4 - (-4) )^2+ (4 - 4)^2)}\) = 8 units

L (length) = 8 Units

So, the length of the horizontal sides (x-axis) of the rectangle is 8 units.

then, the top side has length 8 and there are top and bottom sides are equal length, the perimeter is: P = (8+8) + 2W

20 = 16 + 2W

where, L is the length of one of the vertical sides. Solving for L, we get:

W = (20 - 16)/2 = 2

So, the length of the vertical sides (y-axis) of the rectangle is 2 units.

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Answer:

-2x² - 8x - 15

Step-by-step explanation:

-(2x² + 4x + 11) + (-4)

-2x² - 8x - 11 - 4

-2x² - 8x - 15

Answer:

241.2

Step-by-step explanation:

Divide 201 by 10

\(201/10=20.1\)

Multiply 20.1 by 12

\(20.1 * 12 = 241.2\)

The answer is 241.2

Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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Answer:

See explanation.

Step-by-step explanation:

\((6^2)^x = 1\\= 36^x\\= 36^-^1\\= 1.\)

B: Can't solve it, sorry.

Answer:

V_avg = 0.5556 miles/min

V_avg = 0.00926 miles/sec

Step-by-step explanation:

Bonita jogs 2.5 miles west of Vinces' house to school. It took her 15 minutes to arrive.

Speed 1; distance/time = V1 = 2.5/15 = 1/6 miles/min

Furthermore she ran 5 miles to the discount store for personal supplies. This took her 5 minutes.

Thus;

Speed 2; V2 = 5/5 = 1 mile/min

She then slowly walks back to school, which takes her another 10 minutes. Distance from the discount stor to school is 5 miles as stated in speed 2.

Thus;

Speed 3: V3 = 5/10 = ½ mile/min

Her average speed is;

V_avg = (V1 + V2 + V3)/3

V_avg = (1/6 + 1 + ½)/3

V_avg = 10/18 = 0.5556 miles/min

Converting to miles/seconds

60 seconds make 1 minutes, therefore 1 mile/min = 1/60 miles/seconds

Thus;

V_avg = 0.5556 miles/min = 0.5556 × 1/60 miles/sec = 0.00926 miles/sec