Jose and Jenna competed in a bike race. After 30 minutes, Jose had finished 2/3 of the race and Jenna had finished 7/12 of the race. Who had finished more of the race?

Answer:

19 yards

Step-by-step explanation:

A square has 4 equal sides, thus its area is given by the formula below.

[tex]\boxed{\text{Area of square}=\text{side}^2}[/tex]

Substitute the area of the square into the formula:

361= side²

Square root both sides:

Length of each side

= [tex]\sqrt{361}[/tex]

= 19 yards

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1

The given angle is opposite the longest given side, so there will be exactly one solution.

_____

The number of solutions may be 0, 1, or 2 when the given angle is opposite the shortest given side.

Answer:

13.8–14.2 inches

Step-by-step explanation:

If you assume the "symmetrical and bell-shaped" distribution is a normal distribution, then 95% of observations will lie within 2 standard deviations of the mean:

... 14 in ±2×(0.1 in) = 13.8 in to 14.2 in

Answer:

The total length of the road after the crew has worked 31 days is 183 miles.

Step-by-step explanation:

As given

A construction crew is lengthening a road.

The road started with a length of 59 miles, and the crew is adding 4 miles to the road each day.

let L represent the total length of the road (in miles).

let D represent the number of days the crew has worked.

Than the equation becomes

L = 59 + 4D

Now find out the total length of the road after the crew has worked 31 days.

D = 31 days

Put in the equation

L = 59 + 4 × 31

  = 59 + 124

L  = 183 miles

Therefore the total length of the road after the crew has worked 31 days is 183 miles.

x = 4; y = 9; length of a side = 5

Here, you're expected to use the fact that all of the sides of a square are the same length.

The left and right sides both have different expressions only in y, so it is convenient to equate them.

... y -4 = 2y -13

... 0 = y -9 . . . . . subtract the left side

... 9 = y . . . . . . . add 9

This tells us the side of the square (s) is ...

... s = y -4 = 9 -4

... s = 5

And we can use this to find x.

... 5 = 2x -3 . . . . equate the x-expression to the square side length

... 8 = 2x . . . . . . add 3

... 4 = x . . . . . . . . divde by the coefficient of x

x and y are 4 and 9; the square side length is 5.

The values of x and y are not given, so the length of the square cannot be determined.

To find the side lengths of the square, we first need to determine the values of x and y. However, the provided information does not give any equations or context to solve for x and y. Without additional information, it is not possible to find the values of x and y, and therefore, we cannot calculate the length of the square. If you have any additional information or equations, please provide them so that we can assist you further.

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Answer:

Option C is correct.

The value of x nearest to tenth is, 21.4 units

Step-by-step explanation:

In a given right angle triangle;

by definition of tangent ratio i,e   [tex]\tan \theta = \frac{opposite side}{Adjacent side}[/tex]

[tex]\tan 25^{\circ} = \frac{10}{x}[/tex]

[tex]0.46630765815 = \frac{10}{x}[/tex]

or

[tex]x = \frac{10}{0.46630765815} = 21.4450692[/tex] units

Therefore, the value of x nearest to tenth is, 21.4 units

Answer:

k = -2

Step-by-step explanation:

The graph clearly shows the y-intercept of f(x) as being 4, and that of g(x) as being 2. Thus, g(x) = f(x) -2 = f(x) +k.

Subtracting f(x) from that equation, you get k = -2.

_____

Check

g(x) is displaced 3 units to the right of f(x). The slopes of both f(x) and g(x) are 2/3, so a displacement of 3 units right is equivalent to a displacement of 2 units down. k represents the vertical translation, so is -2.

The value of k is found by examining the vertical distance between the graphs of y=f(x) and y=g(x) at the same x-coordinate. Without the visual graphs or specific points, the exact value of k cannot be provided.

The student is asking about the relationship between two functions, where g(x) is related to f(x) by the addition of a constant k.

To find the value of k, one would typically examine the vertical distance between the two function graphs at any given x-coordinate, since g(x) = f(x) + k. Without the graphical information provided, it is not possible to determine the exact value of k.

However, typically if you have two functions with graphs that are vertically shifted versions of each other, and you know two corresponding points on each graph with integer coordinates, you can subtract the y-values of these points to find k.

Answer:

18 cm

Step-by-step explanation:

The length of the median is the average of the two base lengths:

... (24 cm + 12 cm)/2 = 18 cm

Answer:

34

Step-by-step explanation:

3 + 4 = 7

34 with reversed digits is 43

43 - 34 = 9

1:00 a.m. (and 3:00 a.m., and 5:00 a.m.)

The problem is to find the least common multiple (LCM) of the barking intervals. One way to find the LCM is to find the product of the factors of the numbers.

... 5 = 5 . . . . a prime number

... 8 = 2³

... 12 = 2²×3

The factor 2³ is a multiple of the factor 2², so we only need 2³ in our final product.

The LCM is then ...

... 2³×3×5 = 120 . . . . minutes

The dogs will all bark together every 120 minutes (2 hours).

2 hours after 11 p.m. is 1 a.m.

_____

The problem statement doesn't say whether Ms. Li was awakened multiple times. The dogs will bark together again at 3 a.m., 5 a.m. and (possibly) 7 a.m.

The time when Ms. Li was awakened by the dogs Lola, Patch and Lady barking together was calculated using the concept of least common multiple (LCM). The LCM of the intervals the dogs bark (5, 8, and 12 minutes) is 120 minutes or 2 hours. Therefore, Ms. Li was awakened at 1:00 am.

This problem is a least common multiple (LCM) problem in Mathematics. The dogs Lola, Patch, and Lady started barking together at 11:00 pm. Lola barked every 5 minutes, Patch every 8 minutes, and Lady every 12 minutes. The number that is divisible by all of 5, 8, and 12 is their LCM.

To find the LCM of 5, 8, and 12, list the multiples of each number. The LCM is the smallest number that occurs in each list. In this case, the LCM is 120.

So they all barked together 120 minutes, or 2 hours, after 11:00 pm. Therefore, Ms. Li was awakened at 1:00 am.

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Answer:

2x³y

Step-by-step explanation:

Put the coefficient first; combine the exponents of repeated variables; write the expression with the variables in alphabetical order (not essential, but it lends consistency).

= 2·x^(1+2)·y

= 2x^3·y

To write the expression xycdot 2x² as a monomial, multiply the coefficients and add the exponents of like terms, resulting in 2x³y.

When writing the expression xy cdot 2x²as a monomial in standard form, you should apply the associative property of multiplication and combine like terms. To do this, multiply the coefficients together and add the exponents of the like bases.

Firstly, the coefficients 1 (implied for xy) and 2 should be multiplied, giving us 1 cdot 2 = 2. Then, combine the variables by adding the exponents: x¹cdot x² (since x is equivalent to x¹) becomes x⁽¹⁺²⁾, which simplifies to x³. As there is only one instance of y in the expression, its exponent remains 1. Therefore, the final expression in standard form is 2x³y.

The answer, I believe, is an Equilateral triangle.

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.

the simplified expressions are:

1. [tex](2/3) * x^2 * (1/y) * (1/z^7)[/tex]

2. [tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]

3. [tex](2/3) * (x^2 / y) * (1/z^7)[/tex]

4. [tex](2/3x^2) * yz[/tex]

5. [tex](2x^4 * y) / (3z)[/tex]

Let's simplify each of the given expressions using properties of exponents:

1. [tex](2x^4 * y^-4 * z^-3) / (3x^2 * y^-3 * z^4)[/tex]

To simplify this expression, you can use the properties of exponents that state when you divide two terms with the same base, you subtract the exponents:

[tex](2x^4 / 3x^2) * (y^-4 / y^-3) * (z^-3 / z^4)[/tex]

Now, simplify each term separately:

[tex](2/3) * (x^(4-2)) * (y^(-4-(-3))) * (z^(-3-4))[/tex]

[tex](2/3) * x^2 * y^(-1) * z^(-7)[/tex]

The simplified expression is

[tex](2/3) * x^2 * (1/y) * (1/z^7)[/tex]

2. [tex](3x^2 * y^2 * z^4) / 2[/tex]

To simplify this expression, simply divide each term by 2:

[tex](3x^2 / 2) * (y^2 / 2) * (z^4 / 2)[/tex]

The simplified expression is:

[tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]

3. [tex](2x^2) / (3y * z^7)[/tex]

To simplify this expression, divide each term in the numerator by 3y and each term in the denominator by 3y:

[tex](2x^2) / (3y * z^7) = (2x^2 / 3y) * (1 / z^7)[/tex]

The simplified expression is:

[tex](2/3) * (x^2 / y) * (1/z^7)[/tex]

4. [tex](2yz) / (3x^2)[/tex]

To simplify this expression, divide each term in the numerator by 3x^2:

[tex](2yz) / (3x^2) = (2 / 3x^2) * yz[/tex]

The simplified expression is:

[tex](2/3x^2) * yz[/tex]

5. [tex](2x^4 * y) / (3z)[/tex]

This expression is already in a relatively simple form, and there are no common factors to further simplify it.

So, the simplified expressions are:

1. [tex](2/3) * x^2 * (1/y) * (1/z^7)\\[/tex]

2. [tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]

3.[tex](2/3) * (x^2 / y) * (1/z^7)[/tex]

4. [tex](2/3x^2) * yz[/tex]

5. [tex](2x^4 * y) / (3z)[/tex]

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Answer:

1/8

Step-by-step explanation:

When there are two possiblities for each of 3 positions, the number of possible codes is 2^3 = 8. Your code is one of those, so its probability of occurrence is 1/8.

_____

CCC, CCP, CPC, CPP, PCC, PCP, PPC, PPP

Answer: [tex]\dfrac{1}{8}[/tex]

Step-by-step explanation:

Given: A three-character code uses the letters C and P.

If repetition is allowed then the total number of ways to make the three letter character code using two letters C and P is given by :-

[tex]2\times2\times2=8[/tex]

Since the PCP is one of the character code, therefore , the probability of the code PCP is given by :-

[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{1}{8}[/tex]

Hence, the probability of the code PCP = [tex]\dfrac{1}{8}[/tex]

D. an = 14 - 1.5n

Selection D is the only one that works to give a1 = 12.5.

The explicit rule for the given sequence is option D, an = 14 - 1.5n, which indicates starting from 14, subtract 1.5 times the position of the term (n).

To determine the explicit rule for the given sequence 12.5, 11, 9.5, 8, 6.5, 5, we can observe that the sequence is decreasing by 1.5 each time. Knowing this, we can try to find a relationship between the position of each term (n) and its value (an).

Let's consider the first term when n=1. We need a starting point (initial value when n=1) that degreases by 1.5 for each subsequent term. We can see that the first term of the sequence (12.5) is 1.5 less than 14, so we subtract 1.5 from 14 to define the first term: 14 - 1.5*1 = 12.5. Thus, for any term n, the value would be 14 - 1.5*n.

Therefore, the correct explicit rule is given by option D: an = 14 - 1.5n.

Equilateral

An equilateral triangle has medians that are also angle bisectors that are also altitudes.

Answer: The answer is c)5

Answer:

c) 5

Step-by-step explanation:

A point belongs to the x axis if its y coordinate equals zero.

The points on a graph are in the form [tex] (x,f(x)) [/tex], so these points are on the x axis if and only if [tex] f(x)=0 [/tex]

In this case, we have

[tex] f(x) = 0 \iff x^2+14x+49=0 [/tex]

You can observe that your expression is actually a squared binomial: using

[tex] (a+b)^2 = a^2+2ab+b^2 [/tex]

you can notice that

[tex] (x+7)^2 = x^2+14x+49 [/tex]

So, you have

[tex] x^2+14x+49=0 \iff (x-7)^2 = 0 \iff x=7 [/tex]

Now, how we decide if this function "touches" or "passes through" the x-axis at x=7? Well, since our function is a square, it is never negative. So, this graph can't cross the x-axis, but rater touch it from above. The parabola has a U shape, and the point of minimum lies on the x axis.

So, the graph touches the x axis at x=7.

The graph of the function f(x)=x^2+14x+49 is a parabola that touches the x-axis at -7, it does not pass through it because the root of the equation -7 is of multiplicity 2.

The function f(x)=x^2+14x+49 is a quadratic function, which when factorized becomes f(x) = (x+7)^2. This means that the graph of the function touches the x-axis at -7, but does not pass through it because the root of this equation -7 is of multiplicity 2. Hence, the correct answer is B: The graph touches the x-axis at -7.

To visualize this, remember that a quadratic function like this one forms a parabola. The point where the parabola intersects or touches the x-axis corresponds to the solution(s) of the equation. In this case, because there's only one solution (x=-7), the parabola just touches the x-axis at this point, but doesn't cross it.

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Answer:

[tex]\sqrt{3}[/tex] :1

Step-by-step explanation:

Ratio of height of two cylinders are 3:1

Let C2 has the height x

then height of C1 is 3x

Let r1 is the radius of C1

and r2 is the radius of C2

As given that volume of both are equal

Also we know that formula for the volume of the cylinder is

V= π r²h

for C1

V= π (r1)²h

for C2

V=π (r2)²h

As volume of both are same so equating them

π (r1)²h1 = π (r2)²h2

as h1 =3x and h2=x

putting values

π (r1)²(3x) = π (r2)²(x)

cancelling out π and x from both side of the equation

3(r1)²= (r2)²

Taking square root of both sides give

[tex]\sqrt{3(r1)^{2} }=\sqrt{(r2)^{2} }[/tex]

r1 ( [tex]\sqrt{3}[/tex]) = r2

or

r1 : r2 =  [tex]\sqrt{3}[/tex]  :1

Answer:

C none of the above

Step-by-step explanation:

-7 / -f

We know that a negative divided by a negative is a positive

-1/-1  * 7/f

1* 7/f

7/f

the tale-tell fellow is the base of the exponent ˣ.

if that number is less than 1, is a decay factor, if it's more than 1, is growth.

1.09 is cleary more than 1, so is growth, at what rate?

[tex]\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &P\\ r=rate\to r\%\to \frac{r}{100}\dotfill &0.0r\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ f(x)=4.7(1.09)^x\implies f(x)=4.7(1+\stackrel{\stackrel{r}{\downarrow }}{0.09})^x \\\\\\ r=0.09\implies \stackrel{\textit{converting it to percentage}}{r=0.09\cdot 100}\implies r=\stackrel{\%}{9}[/tex]

Exponential functions are mostly used to represent growth of population.

The true option is: (d)  Exponential growth function; 9%

The function is given as:

[tex]\mathbf{f(x) = 4.7 \cdot 1.09^x}[/tex]

An exponential function is represented as:

[tex]\mathbf{f(x) = a \cdot b^x}[/tex]

By comparison:

[tex]\mathbf{b = 1.09}[/tex]

When b is greater than 1, then the function is a growth function.

Next, we calculate the constant percentage rate of growth (r)

If b is greater than 1, then:

[tex]\mathbf{b = 1 + r}[/tex]

Substitute 1.09 for b

[tex]\mathbf{1 + r = 1.09}[/tex]

Subtract 1 from both sides

[tex]\mathbf{r = 0.09}[/tex]

Express as percentage

[tex]\mathbf{r = 0.09 \times 100\%}[/tex]

[tex]\mathbf{r = 9\%}[/tex]

Hence, the growth rate is 9%

Hence, the true option is: (d)  Exponential growth function; 9%

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Answer:

D

Step-by-step explanation:

a) correct is 3/4.5=4/6; b) correct is 3.2/2.4=4/3; c) correct is 4/3.2=3/2.4; d) this is correct answer.

y = -4.2x +34

The differences between adjacent y-values are -4.2 for all data points given, so the data is best modeled by a linear function with a slope of -4.2. The value for x=0 (the y-intercept) will be 4.2 higher than the value for x=1, so will be 34.

Thus the model can be ...

... y = -4.2x + 34

_____

Comment on the attached graph

The graph shows an attempt to model the data with a quadratic function (the first on your answer list). The result is that the x² coefficient is zero, and the model is the equation of a line (as shown above).

Answer:

Linear

Step-by-step explanation:

I got it from passing a quiz

Answer:

B. b = 11 3/5

Step-by-step explanation:

-3 2/5 + b = 8 1/5

The first step is to isolate b by adding 3 2/5 to each side

-3 2/5+ 3 2/5 + b = 8 1/5 + 3 2/5

b = 8 1/5 + 3 2/5

b = 8+3  + 1/5+2/5

b = 11  3/5

Answer:

k = -3

Step-by-step explanation:

Simplify, divide by 9, add the opposite of the constant.

0 = 9k -9·2/3 +33

0 = 9k +27

0 = k +3

-3 = k

Answer:

y=7

Step-by-step explanation:

If you subtract 5 from each side it would be 2y-5=9. Add a 5 back to each side to be 2y=14. Divide each side by 2 to get y=7.

Cos(y-z) = Cos(z-24)

You have two equations in three unknowns, so no solution for the unknowns is possible.

The tangent equation tells you ...

... tan(z -24) = tan(y -z)

... z -24 = y -z . . . . . . take the arctangent

... cos(y -z) = cos(z -24) . . . . take the cosine

Answer:

A. 1⁄2 < 3⁄4

Step-by-step explanation:

1/2   vs 3/4

Get a common denominator of 4

1/2 *2/2   vs 3/4

2/4   vs 3/4

2 is less than 3

2/4 < 3/4

1/2 < 3/4

Answer:

See below

Step-by-step explanation:

The values in the table change by $3.80 from one line to the next. Since each change from line to line changes in number of photos by 20, the average cost per photo is $3.80/20 = $0.19. There is apparently a $5.80 -3.80 = $2.00 shipping charge for numbers of photos in the range shown in the table.

Thus, the piecewise function has 3 pieces:

for x < 100: $2.00 + 0.19x

for x < 200: $4.50 + 0.17x

for x ≥ 200: $0.15x

This could be written as ...

[tex]C(x)=\left\{\begin{array}{rcl}\$2.00+0.19x&\text{for}&0\le x<100\\\$4.50+0.17x&\text{for}&100\le x<200\\\$0.15x&\text{for}&x\ge 200\end{array}\right.[/tex]