What is the volume, in cubic centimeters, of a cube whose side measures 4 centimeters ?

Fill in the blank by entering only a number as your answer.

Using the together rate, it is found that it would take each person working individually 27 and 29 hours to paint the house.

The together rate is the sum of each separate rate.

In this problem, we have that the rates are given as follows:

Hence:

[tex]\frac{1}{d} + \frac{1}{d - 2} = \frac{1}{14}[/tex]

[tex]\frac{d - 2 + d}{d(d - 2)} = \frac{1}{14}[/tex]

d² - 2d = 28d - 28.

d² - 30d + 28 = 0

(d - 29)(d - 0.96) = 0.

Both d and d - 2 have to be positive, hence the solution is d = 29, and it would take each person working individually 27 and 29 hours to paint the house.

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Answer:

Step-by-step explanation:jneke

There is no such value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.

Two polynomials are said to be equivalent only when the coefficients of all powers of x are equal for both the polynomials.

In the question, we are asked is there a value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.

We know that two polynomials are said to be equivalent only when the coefficients of all powers of x are equal for both the polynomials.

Thus to check, we expand g(x), using the formula (p - q)² = p² + q² - 2pq.

g(x) = (3x - a)²,

or, g(x) = (3x)² + (a)² - 2(3x)(a),

or, g(x) = 9x² + a² - 6ax.

For f(x) = 9x² - 4, and g(x) = (3x - a)² to be equivalent,

As we need two different values of, 'a' at the same time, which ain't possible, thus we can say that there is no such value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.

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Answer:

? = 38°

Step-by-step explanation:

We can use the property of sine to find the missing angle value.

sin (angle) = opposite / hypotenuse

sin (?) = 16 / 26                                  <----- Insert values

? = sin⁻¹(16 / 26)                                 <----- Rearrange

? = 37.97...                                         <----- Solve

? = 38°                                               <----- Round

The derivative of the natural logarithm function is given by:

[tex]f^{\prime\prime}(x) = \cotg{x}[/tex]

Suppose we have a composite natural logarithm function given as follows:

[tex]f(x) = \ln{g(x)}[/tex]

The derivative of the function is given as follows:

[tex]f^{\prime}(x) = \frac{g^{\prime}(x)}{g(x)}[/tex]

In this problem, the function, which is already a first derivative, it given by:

[tex]f^{\prime}(x) = \ln{|\sin{x}|} + 3[/tex]

The derivative of a constant is of zero, and the derivative of sin(x) is cos(x), hence the derivative of the entire function is given as follows:

[tex]f^{\prime\prime}(x) = \frac{\cos{x}}{\sin{x}} = \cotg{x}[/tex]

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The correct option is Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction

Emanuel did a mistake in her first step by taking negative sign twice.

Positive results are obtained if the sign are same. If the signs disagree, the outcome is adverse. Addition: Keep in mind that a signed number's magnitude and absolute value are the same.

Multiplication and division appear to be more difficult than addition and subtraction, but they are actually far less challenging. The result of multiplying two positive or two negative numbers with the same sign, according to the rule, will always be positive.

For instance:

According to question,

= [tex]\left(\frac{3}{5}\right)\left(\frac{4}{9}\right)\left(-\frac{1}{2}\right)[/tex]

Emanuel found the solution, but she erred in the first step. She incorrectly distributes the negative sign with both 1 and 2, as she should. We can write negative sign with either 1 or 2 but not both.

Correct steps are:

Step 1:

[tex]\frac{(3)(4)(-1)}{(5)(9)(2)}[/tex]

Step 2:

[tex]\frac{-12}{90}[/tex]

Step 3:

[tex]-\frac{2}{15}[/tex]

Therefore, the step 1 was miscalculated by Emanuel.

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The complete question is -

Emanuel used the calculations below to find the product of the given fractions. (Three-fifths) (StartFraction 4 over 9 EndFraction) (Negative one-half)

Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction Step 2 StartFraction negative 12 over negative 90 EndFraction

Step 3 StartFraction 12 over 90 EndFraction

Step 4 StartFraction 2 over 15 EndFraction

In which step did his first error occur?

Question 8

1) [tex]\triangle ACE[/tex] with [tex]\overline{AC} \cong \overline{EC}[/tex], [tex]\overline{BC} \cong \overline{DC}[/tex] (given)

2) [tex]\angle C \cong \angle C[/tex] (reflexive property)

3) [tex]\triangle ACD \cong \triangle ECB[/tex] (SAS)

Question 9

1) [tex]\overline{PQ}[/tex] and [tex]\overline{PR}[/tex] are the legs of isosceles [tex]\triangle PQR[/tex], [tex]\overline{PS} \cong \overline{QR}[/tex] (given)

2) [tex]\angle PSQ[/tex] and [tex]\angle PSR[/tex] are right angles (definition of perpendicular lines)

3) [tex]\angle Q \cong \angle R[/tex] (angles opposite the legs of an isosceles triangle are congruent)

4) [tex]\overline{PS} \cong \overline{PS}[/tex] (reflexive property)

5) [tex]\angle PSQ \cong \angle PSR[/tex] (all right angles are congruent)

6) [tex]\triangle PSQ \cong \triangle PSR[/tex] (AAS)

Question 10

1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AB} \perp \overline{BC}[/tex], [tex]\overline{CD} \perp \overline{AD}[/tex] (given)

2) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)

3) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\triangle ABC[/tex] and [tex]\triangle ADC[/tex] are right triangles (a triangle with a right angle is a right triangle)

5) [tex]\triangle ABC \cong \triangle CDA[/tex] (HL)

6) [tex]\overline{AD} \cong \overline{CB}[/tex] (CPCTC)

Answer:

0.35 km per minute, 7 km in 20 minutes

Step-by-step explanation:

1 hr = 60 minutes

21 km per 60 minutes = 21/60 = 0.35 km per minute

In 20 minutes: 0.35*20 = 7 km

Answer: G=4

Step-by-step explanation:

A population of a particular yeast cell develops with a constant relative growth rate of [tex]0.4311[/tex] per hour. The initial population consists of [tex]3.9[/tex]million cells. Find the population size (in millions of cells) after 5 hours. Population size after [tex]5hrs[/tex]  is  [tex]33.6million[/tex].

How can we find the population size ?

The projection of population growth in yeast is given by

[tex]N=N_{0} e^{rt}[/tex]

Where [tex]N_{0}[/tex]=initial population which is [tex]3.9million[/tex]

[tex]r[/tex]=intrinsic rate of natural increases which is [tex]0.4311million per hour[/tex]

N is population size

Substitute the values

[tex]N=N_{0} e^{rt}\\N=3.9(e^{0.4311*5} )\\\\N=33.6 million[/tex]

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There is no change in the temperature.

To find how much temperature is changed:

Let, 'F' be the temperature.

Temperature decreased by [tex]33\frac{1}{3}[/tex]%.

F × (1-.33333) = Temperature increases by 50%.

(F × (1-.33333)(1.50)) = F =  No net change, right back to the original temperature F.

Therefore, there is no change in the temperature.

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Answer:

Step-by-step explanation:

A + B= 180°

(5x+20)+(9x-92)=180°

14x-72=180°

14x=252

x=18

A=5(18)+20

A=110

Answer:

x = 18 , ∠ A = 110°

Step-by-step explanation:

∠ A and ∠ B are same- side interior angles and sum to 180° , that is

5x + 20 + 9x - 92 = 180

14x - 72 = 180 ( add 72 to both sides )

14x = 252 ( divide both sides by 14 )

x = 18

Then

∠ A = 5x + 20 = 5(18) + 20 = 90 + 20 = 110°

Answer:

∠α = 5.001°

a easy calculator for this is:

https://www.calculator.net/right-triangle-calculator.html?av=3.5&alphav=&alphaunit=d&bv=40&betav=&betaunit=d&cv=&hv=&areav=&perimeterv=&x=57&y=16

The slope intercept form of the line whose points are (1,5) and (-2,-4) is y=3x+2.

Given two points of a line (1,5) and (-2,-4).

We have to form an equation in slop intercept form.

Equation is relationship between two or more variables which are expressed in equal to form.Equations of two variables looks like ax+by=c.

Point slope form of an equation is y=x+mc where m is slope of the line.

From two points the formula of equation is as under:

(y-[tex]y_{1}[/tex])=[tex](y_{2} -y_{1} )/(x_{2} -x_{1} )[/tex]*(x-[tex]x_{1}[/tex])

where [tex](x_{1} ,y_{1} ) and (x_{2} ,y_{2} )[/tex] are the points.

Putting the values of [tex]x_{1}[/tex]=1, [tex]x_{2}[/tex]=-2, [tex]y_{1}[/tex]=5 and [tex]y_{2}[/tex]=-4.

y-5=(-4-5/-2-1)*(x-1)

y-5=-9/-3*(x-1)

y-5=3(x-1)

y-5=3x-3

y=3x-3+5

y=3x+2

Hence the slope intercept form of the line having points (1,5)(-2,-4) is y=3x+2.

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Check the picture below.

we could also look at it from the inscribed angle theorem, bearing in mind that the intercepted arc is 180°.

Q1

Nominal - D

Ordinal-  B, G

Ratio - A, C, E, F

Q2

Quantitative- A, C, D, G

Qualitative -B, E, F, G

Q3

Simple Random - A, C

Systematic Sample - B

Nominal measures are the most accurate and meaningless, as they only show the "characteristics" or "identities" that we are interested in. In other words, in a nominal variable, a number just gives the attribute a unique "name". In this case, the number is just a label.

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Answer:

The equation should be 2.5x+1.8=59.3

Step-by-step explanation:

The number of miles in the taxi ride is 10

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

Dalvin took a taxi from his house to the house. The taxi company charged a pick-up fee of $4.80;

The fare per mile is $2

The total fare was $30.80, not including the tip;

Let the number of mile is x

Total fare = pick up fee + fee per mile

30.80 = 4.80 + 2x

2x = 26

x = 13

Therefore, the number of miles by algebra Dalvin took a taxi will be 13

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The rate at which the water from the container is being drained is 24 inches per second.

Given radius of right circular cone 4 inches .height being 5 inches, height of water is 2 inches and rate at which surface area is falling is 2 inches per second.

Looking at the image we can use similar triangle propert to derive the relationship:

r/R=h/H

where dh/dt=2.

Thus r/5=2/5

r=2  inches

Now from r/R=h/H

we have to  write with initial values of cone and differentiate:

r/5=h/5

5r=5h

differentiating with respect to t

5 dr/dt=5 dh/dt

dh/dt is given as 2

5 dr/dt=5*-2

dr/dt=-2

Volume of cone is 1/3 π[tex]r^{2} h[/tex]

We can find the rate at which the water is to be drained by using partial differentiation on the volume equation.

Thus

dv/dt=1/3 π(2rh*dr/dt)+([tex]r^{2}[/tex]*dh/dt)

Putting the values which are given and calculated we get

dv/dt=1/3π(2*2*2*2)+(4*2)

=1/3*3.14*(16+8)

=3.14*24/3.14

=24 inches per second

Hence the rate at which the water is drained from the container is 24 inches per second.

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The inequality passing through (1, 4), (-2, -2), intersecting the y-axis at 2 units and intersects the x-axis at (-1, 0) to form shaded portions on the left side is y > 2x+2

An equation is an expression that shows the relationship between two or more variables and numbers.

An inequality shows the non equal comparison of two or more numbers and variables.

The inequality passing through (1, 4), (-2, -2), intersecting the y-axis at 2 units and intersects the x-axis at (-1, 0) to form shaded portions on the left side is y > 2x+2

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The length of the square pool is 8. 49cm

Note that the formula for finding the area of a square is given as;

Area = length^2

We have

Area = 72 m²

Substitute into the formula

I^2 = 72

Find the square root of both sides

I= √72

I = 8. 49cm

The length of the square pool given as I is 8. 49cm

Thus, the length of the square pool is 8. 49cm

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[tex]\textbf{Heya !}[/tex]

✏[tex]\bigstar\textsf{Given:-}[/tex]✏

✏[tex]\bigstar\textsf{To\quad find:-}[/tex] ✏

▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪

✏[tex]\bigstar\textsf{Solution\quad steps:-}[/tex] ✏

If y is inversely proportional to x^2, the equation looks as shown below:-

[tex]\sf{\longmapsto{y=\cfrac{k}{x^2}}[/tex], where k -- constant of proportionality

Plug in all values

[tex]\sf{\longmapsto{2=\cfrac{k}{4^2}}[/tex] , simplifying --

[tex]\sf{\longmapsto{2=k/16}[/tex]

multiply by 16 both sides

[tex]\sf{\longmapsto 2*16=k}}[/tex]

[tex]\sf{\longmapsto{32=k}}[/tex]

▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪

Plug 32 into the second equation:-

[tex]\sf{\longmapsto y=\cfrac{32}{\bigg(\cfrac{1}{2}\bigg)^2}}[/tex]

simplify the complex fraction

[tex]\longmapsto\sf{y=\cfrac{32}{\cfrac{1}{4}}[/tex]

divide fractions

[tex]\sf{\longmapsto{y=\cfrac{32}{1}\div\cfrac{1}{4}}=\cfrac{32}{1}\cdot}\cfrac{4}{1}}=128}[/tex]

`hope that was helpful to u ~

When two or more given triangles are congruent, this implies that the measures of their corresponding angles and sides are equal. So that the additional information required in the question is FG ≅ IJ.

When two or more given triangles are congruent, this implies that the measures of their corresponding angles and sides are equal. Thus the congruent relations of the triangles can be with respect to their angles or/ and sides.

The two given triangles in the question would be congruent with respect to the Side-Angle-Side (SAS) postulate if the condition below is true:

i.e FG ≅ IJ

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The domain and range of the graph of a logarithmic function are;

The basic equation of a logarithmic function can be presented in the form;

[tex]y = log_{b}(x) [/tex]

Where;

b > 0, and b ≠ 1, given that we have;

[tex]y = log_{1}(x)[/tex]

[tex] {1}^{y} = 1[/tex]

The inverse of the logarithmic function is the exponential function presented as follows;

[tex]x = {b}^{y} [/tex]

Given that b > 0, we have;

[tex] {b}^{y} = x > 0[/tex]

Therefore, the graph of a logarithmic function has only positive x-values

The graph of a logarithmic function is one with a domain and range defined as follows;

Domain; 0 < x < +∞

Range; -∞ < y < +∞, which is the set of real numbers.

The correct option therefore has a domain as x > 0 and range as the set of all real numbers.

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Answer:

3 or C

Step-by-step explanation:

The answer above is correct.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation \#1.}[/tex]

[tex]\mathsf{|-8| + 9 = }[/tex]

[tex]\huge\textbf{Random note:}[/tex]

[tex]\textsf{The additive inverse of }\mathsf{|-8|}\textsf{ is positive 8.}[/tex]

[tex]\huge\textbf{Solving for the equation:}[/tex]

[tex]\mathsf{|-8| + 9}[/tex]

[tex]\mathsf{= \bold 8 + 9}[/tex]

[tex]\mathsf{= 17}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{17}}\huge\checkmark[/tex]

[tex]\huge\textbf{Equation \#2.}[/tex]

[tex]\mathsf{|-8 + 9| =}[/tex]

[tex]\huge\textbf{Random note:}[/tex]

[tex]\textsf{We will convert your equation to }\mathsf{-8 + 9}\textsf{ because it can make the equation}\\\textsf{a lot easier to solve.}[/tex]

[tex]\huge\textbf{Solving for the equation:}[/tex]

[tex]\mathsf{|-8 + 9|}[/tex]

[tex]\mathsf{= -8 + 9}[/tex]

[tex]\text{Start at }\rm{-8}\text{ and go \boxed{up} 9 spaces to the right and you have your answer.}[/tex]

[tex]\mathsf{= 1}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The polynomial function in standard form that has the zeros listed. i and -i is  x² +1 = 0.

A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions.

The values of x that fulfil the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.

Calculation for the polynomial function-

The general two degree/quadratic equation is given by-

ax² + bx + c = 0

Where a ≠ 0

If the two roots of the equation are x1 and x2.

Then the relation between roots and coefficients of the polynomial are -

         x1 + x2 = (-b)/a

        x1.x2 = c/a

From the above two relation the general equation can be written as-

x² -(x1 - x2)x + x1.x2 = 0

Lets say x1 = i and x2 = -i

Substitute the values of x1 and x2 in the general equation

x² -(i - i)x + (i).(-i) = 0

x² - i ² = 0

x² + 1 = 0

Therefore, the polynomial function in standard form that has the zeros listed. i and -i is x² + 1 = 0.

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The correct answer is none of the above.

A line is defined as the shortest distance between two points and the point  where two lines meet is known as an angle.

From the given figure, the measure of angle a and b are supplementary since the sum of the angles is not 180 degrees.

They are not vertical angles since they do not meet at a point of intersection

The measure of angle a and b are complementary since the sum of the angles is not 90 degrees. Hence the correct answer is none of the above.

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Answer:

See attached image

Step-by-step explanation:

The confidence interval formula is extremely complicated to derive, which is one of the justifications for using the bootstrap approach. this statement is true.

A resampling technology named the bootstrap can be used to sample a dataset using replacement to calculate statistics on a group. Estimating summary statistics like the mean or standard deviation may be done using it.

The benefits of bootstrapping include its simplicity in estimating standard errors and confidence intervals as well as its cost-effectiveness in avoiding the need to conduct the operation to get additional groups of sampled data.

Therefore it can be concluded that the said query statement is true.

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Answer:

base = 12 cm , altitude = 16 cm

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] ba ( b is the base and a the altitude )

here a = b + 4 , then

[tex]\frac{1}{2}[/tex] b(b + 4) = 96 ( multiply both sides by 2 to clear the fraction )

b(b + 4) = 192

b² + 4b = 192 ( subtract 192 from both sides )

b² + 4b - 192 = 0 ← in standard quadratic form

(b + 16)(b - 12) = 0 ← in factored form

equate each factor to zero and solve for b

b + 16 = 0 ⇒ b = - 16

b - 12 = 0 ⇒ b = 12

however, b > 0 then b = 12

so base = 12 cm and altitude = b + 4 = 12 + 4 = 16 cm

Answer:

base = 12 cm

Altitude = 16 cm

Step-by-step explanation:

        [tex]\sf \boxed{Area \ of \ triangle = \dfrac{1}{2}*base*height}[/tex]

base = x cm

altitude or height = (x + 4) cm

[tex]\sf \dfrac{1}{2}*x*(x+4) = 96\\\\[/tex]

x * (x + 4) = 96*2

x*x + x*4 = 192

x² + 4x   = 192

x² + 4x - 192 = 0

Sum = 4

Product = -192

Factors =  (-12) , 16

When we add (-12) & 16, we get 4. When we multiply (-12) & 16, we get (-192).

Rewrite the middle term using the factors.

x² + 16x - 12x - 192 = 0

x(x + 16) -12(x + 16) = 0

(x + 16)(x - 12) = 0

x - 12 = 0     or x + 16 = 0

x = 12             or x = -16

Ignore x = -16 as measurements won't be in negative value.

x = 12

Base = 12 cm

Altitude = 12 + 4 = 16 cm

1) JKLM is a parallelogram, [tex]\overline{KL} \cong \overline{LM}[/tex] (given)

2) JKLM is a rhombus (a parallelogram with a pair of consecutive congruent sides is a rhombus)