Find the discriminant
9x^2+14x+13=8x^2

The required students will need to make 10 tiles to create a row that is 4 feet 2 inches long.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.

Here,

To solve this problem, we first need to convert the length of the row from feet and inches to inches.

4 feet 2 inches is equal to (4 x 12) + 2 = 50 inches.

Next, we can divide the length of the row by the length of each tile to find the number of tiles needed:

Number of tiles = Length of row / Length of each tile

Number of tiles = 50 inches / 5 inches

Number of tiles = 10 tiles

Therefore, the students will need to make 10 tiles to create a row that is 4 feet 2 inches long.

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We have been given that the cost of admission is ​$48 for four pets and ​$96 for eight pets. We are asked to determine the independent variable and the dependent variable in the given linear relationship.

We can see that as the number of pets is increasing cost of admission is also increasing. This means that cost depends on number of pets.

Therefore, cost of admission is dependent variable and number of pets is independent variable.

To find rate of change, we will use slope formula.

We have been given two points on line that are (4,48) and (8,96).

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Upon substituting the coordinates of our given points in slope formula, we will get:

[tex]m=\frac{96-48}{8-4}[/tex]

[tex]m=\frac{48}{4}[/tex]

[tex]m=12[/tex]

Therefore, the rate of change is $12 per pet.

Answer:

37

Step-by-step explanation:

The first thing is to calculate critical z factor

the alpha and the critical z score for a confidence level of 90% is calculated as follows:

two sided alpha = (100% - 90%) / 200 = 0.05

critical z factor for two sided alpha of .05 is calculated as follows:

critical z factor = z factor for (1 - .05) = z factor for (.95) which through the attached graph becomes:

critical z factor = 2.58

Now we have the following formula:

ME = z * (sd / sqrt (N) ^ (1/2))

where ME is the margin of error and is equal to 6, sd is the standard deviation which is 14 and the value of z is 2.58

N the sample size and we want to know it, replacing:

6 = 2.58 * (14 / (N) ^ (1/2))

solving for N we have:

N = (2.58 * 14/6) ^ 2

N = 36.24

Which means that the sample size was 37.

Answer:

Answer is No, ITS NOT.

Refer below.

Step-by-step explanation:

There are two different cost of the same activity i.e. $10 on Saturday and Sunday and $5 on Monday through Friday, So it wouldn't be a function.

Answer:

Time taken by A = 16 seconds

Time taken by B = 12 seconds

Step-by-step explanation:

Given:

Two elevator and their respective time to reach certain height.

Here time is function of height.

Time taken by elevator A = 0.8(h)+16

Time taken by elevator B = -0.8(h)+12

We have to find the time taken by the elevator to reach ground level.

Accordingly:

We know that ground level the height will be zero meaning that (h=0).

Plugging the h values in the equation we can find the time taken by both the elevators to reach zero height that is the ground level.

⇒ [tex]t_A=0.8h+16[/tex]                      ⇒ [tex]t_B=-0.8h+12[/tex]

⇒ [tex]t_A=0.8(0)+16[/tex]                   ⇒ [tex]t_B=-0.8(0)+12[/tex]

⇒ [tex]t_A=16[/tex] sec                          ⇒ [tex]t_B=12[/tex] sec

So,

Time taken by elevator A and elevator B to reach the ground is 16 seconds and 12 seconds respectively.

Answer:

5.54

Step-by-step explanation:

5.54 is the (MAD)

Answer:

x = 55 degrees.

y = 49 degrees.

Step-by-step explanation:

AB =  AD and BC = DC so we have 2 isosceles triangles here thus the base angles are equal.

Therefore  m < y = (180 - 82)/2 = 98/2

= 49 degrees.

m < x = (180 - 2*35)/2 = 55 degrees.

Answer:

[tex]\frac{16}{28}[/tex]

Step-by-step explanation:

Question asked:

Select all of the ratios that are equivalent to 4 to 7.

1) 5/8

2) 12/10

3) 8.14

4) 5 to 10

5) 16/28

6) 9 to 16​

Solution:

To know the ratios are equivalent to [tex]\frac{4}{7}[/tex] or not, we have to check each by cross multiplication:-

1) [tex]\frac{5}{8}[/tex]

[tex]\frac{4}{7} =\frac{5}{8} \\ \\[/tex]

By cross multiplication:

[tex]4\times8=5\times7\\ \\ 32=35[/tex]

Not equivalent.

2) [tex]\frac{12}{10}[/tex]

[tex]\frac{4}{7} =\frac{12}{10} \\ \\[/tex]

By cross multiplication:

[tex]4\times10=12\times7\\ \\ 40=84[/tex]

Not equivalent.

3) 8.14 = [tex]\frac{814}{100} \ eliminating\ decimal[/tex]

[tex]\frac{4}{7} =\frac{814}{100} \\ \\[/tex]

By cross multiplication:

[tex]4\times100=814\times7\\ \\ 400=5698[/tex]

Not equivalent.

4) [tex]\frac{5}{10}[/tex]

[tex]\frac{4}{7} =\frac{5}{10} \\ \\[/tex]

By cross multiplication:

[tex]4\times10=5\times7\\ \\ 40=35[/tex]

Not equivalent.

5)[tex]\frac{16}{28}[/tex]

[tex]\frac{4}{7} =\frac{16}{28} \\ \\[/tex]

By cross multiplication:

[tex]4\times28=16\times7\\ \\ 112=112[/tex]

Yes, this is equivalent.

6) [tex]\frac{9}{16}[/tex]

[tex]\frac{4}{7} =\frac{9}{16} \\ \\[/tex]

By cross multiplication:

[tex]4\times16=9\times7\\ \\ 64=63[/tex]

Not equivalent.

Thus, only [tex]\frac{16}{28}[/tex] is equivalent.

Answer:

45 hours a week

Step-by-step explanation:

Ok, so we know that he worked 675 hours in 15 weeks.

So all we need to do is divide the hours by the amount of weeks, which is 15:

675/15= 45

So he worked 45 hours a week!

There has been a statistically significant change in the mean length of the candy bars since the computed t value, -2.913, is less than the critical t value of -2.718. Therefore, we reject the null hypothesis that the mean length has not changed.

A hypothesis test is performed to test the claim at the 0.02 level that there has been no change in the mean length of candy bars. The null hypothesis is that the mean length remains 43mm, as given. The alternate hypothesis is that the mean length has changed. A sample of twelve bars is taken and with the given data, the computed t value is -2.913.

For a two-tailed test at the 0.02 significance level and degrees of freedom (n-1) equals 11, the critical t values are -2.718 and 2.718. If the computed t value falls beyond this range, that is, below -2.718 or above 2.718, we reject the null hypothesis. In this case, -2.913 is less than -2.718

Therefore, there has been a statistically significant change in the mean length of the bars as the t value lies in the rejection region.

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The correct option is Yes, because the computed t lies in the rejection region. The t-test analysis indicates a statistically significant change in the mean length of candy bars based on the computed t-value falling in the rejection region.

Null Hypothesis (H0): The mean length of the candy bars is 43 mm.

Alternate Hypothesis (Ha): There has been a change in the mean length of the candy bars.

T-Test Analysis: The computed t-value of -2.913 falls in the rejection region, indicating statistical significance, therefore rejecting the null hypothesis. Hence, there has been a statistically significant change in the mean length of the bars.

Step-by-step explanation:

[tex]0.00026 = 2.6 \times {10}^{ - 4} \\ [/tex]

Answer:

24, -48

Step-by-step explanation:

In this geometric sequence, the previous number is being multiplyed by -2 each time

This said the next number is 24.

-12*-2=24

and the next one is -48.

24*-2=-48

Final answer:

The next two terms of the geometric sequence -3, 6, -12 are 24 and -48, found by repeatedly multiplying with the common ratio of -2.

Explanation:

The first three terms of the given geometric sequence are -3, 6, and -12. To find the next two terms in this sequence, we need to determine the common ratio between the terms. The common ratio (r) is the factor by which we multiply one term to get the next term. In this case, 6 divided by -3 equals -2, and similarly, -12 divided by 6 also equals -2. This confirms that our common ratio is -2.

Now, to find the fourth term of the sequence, we multiply the third term (-12) by the common ratio (-2):

-12 × -2 = 24

To find the fifth term, we multiply the fourth term (24) by the common ratio (-2):

24 × -2 = -48

Therefore, the fourth and fifth terms of the geometric sequence are 24 and -48, respectively.

Step-by-step explanation:

The population of the city of Miami = 463,300

The rate of increase in population every year = 3%

The population of the city after 7 years = ?

By formula, [tex]P_{n} = P (1 +\frac{r}{100})^{n }[/tex]

Pn is the population after 7 years

P is the current population = 463,300

r = 3 %, n = 7

[tex]P_{7} = 463300 (1 +\frac{3}{100})^{7 }[/tex]

= 463300 (1.23)

= 569859

The population of the city after 7 years = 569,859

Answer:

a -pound bag of cat food can enough to feed her cat for 7 days

Step-by-step explanation:

Given:

Number of cat food used in 7 days (in ounces): 7*6 = 42 ounces

As we know,1 pound (lb) is equal to 16 Ounces (oz)

<=> 42 ounces = 42 /16 = 2.625 pounds < 3-pound bag

So a -pound bag of cat food can enough to feed her cat for 7 days

Hope it will find you well.

Answer:

Yes it will

Step-by-step explanation:

Let's first work with a single unit so that our work will be a lot easier.

We are going to convert pounds to ounces and since 1 pound = 16 ounces, 3 pounds = 16 × 3 = 48 ounces of cat food.

And she feeds her cat 6 ounces of food each day,that means that in 7 days the cat will only be able to consume just 7 × 6 = 42 ounces,but remember that the amount of cat food bought is equal to 48 pounds.

This here means that the cat food will be enough to feed the cat for 7 days

Answer:

A = 68 unit^2

Step-by-step explanation:

Given:-

The piece-wise function f(x) is defined over an interval as follows:

                       f(x) =  { x^2+3x+4    , x < 3

                       f(x) =  { x^2+3x+4     , x≥3

                        Domain : [ -3 , 4 ]

Find:-

Find the area of the region enclosed by f(x) and the x axis

Solution:-

- The best way to tackle problems relating to piece-wise functions is to solve for each part individually and then combine the results.

- The first portion of function is valid over the interval [ -3 , 3 ]:      

                       [tex]f(x) = x^2+3x+4[/tex]

- The area "A1" bounded by f(x) is given as:

                      [tex]A1 = \int\limits^a_b {f(x)} \, dx[/tex]

Where,  The interval of the function { -3 , 3 ] = [ a , b ]:

                     [tex]A1 = \int\limits^a_b {x^2+3x+4} \, dx\\\\A1 = \frac{x^3}{3} + \frac{3x^2}{2} + 4x |\limits_-_3^3 \\\\A1 = \frac{3^3}{3} + \frac{3*3^2}{2} + 4*3 - \frac{-3^3}{3} - \frac{3(-3)^2}{2} - 4(-3)\\\\A1 = 9 + 13.5 +12 + 9-13.5+12\\\\A1 =42 unit^2[/tex]

- Similarly for the other portion of piece-wise function covering the interval [3 , 4] :

                     [tex]f(x) = 4x+10[/tex]

- The area "A2" bounded by f(x) is given as:

                      [tex]A2 = \int\limits^a_b {f(x)} \, dx[/tex]

Where,  The interval of the function { 3 , 4 ] = [ a , b ]:

                     [tex]A2 = \int\limits^a_b {4x+10} \, dx\\\\A2 = 2x^2 + 10x |\limits_3^4 \\\\A2 = 2*(4)^2 + 10*4 - 2*(3)^2 - 10*3\\\\A2 = 32 + 40 - 18-30\\\\A2 =26 unit^2[/tex]

- The total area "A" bounded by the piece-wise function over the entire domain [ -3 , 4 ] is given:

                     A = A1 + A2

                     A = 42 + 26

                     A = 68 unit^2

To find the area enclosed by f(x) and the x-axis from x = -3 to x = 4 for the given piecewise function, calculate the integral of each piece separately and then sum the areas. The area is divided into two parts due to the function having different expressions before and after x = 3.

The student is asking to find the area under the curve of a given piecewise function f(x) on the interval from x = -3 to x = 4. Since the function is defined differently for x < 3 and x ≥ 3, the area calculation involves two parts:

The first part can be calculated using the integral of [tex]f(x) = x^2 + 3x + 4[/tex]from x = -3 to x = 3. The second part is the integral of [tex]f(x) = 4x + 10[/tex] from x = 3 to x = 4. The total area is the sum of these two areas. For this function, the areas are bounded above by the function and below by the x-axis, so all areas are considered positive.

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Answer:

Not enough statistical evidence to prove that treatment 2 sample mean u2 is less than treatment 1 sample mean u1. So the claim may be supported.

Step-by-step explanation:

Solution:-

- The sample size of two treatments, n = 16

- The mean of sample treatment 1, u1

- The mean of sample treatment 2 , u2

- The significance level, α = .05

- State the hypothesis:

                      Null hypothesis : u2 - u1 > 0

                      Alternate hypothesis : u2 - u1 ≤ 0

- The rejection region of the T- critical for lower tailed test.

                      significance level, α = .05

                      degree of freedom v = n - 1 = 16 - 1 = 15

                      T-critical =  - 1.75

- The T-test value is compared with T-critical:

                      T-test = 1.94

                      T- critical = -1.75

                      T-test > T-critical  .. ( Null not rejected )

- Not enough statistical evidence to prove that treatment 2 sample mean u2 is less than treatment 1 sample mean u1. So the claim maybe supported.

Answer:

25 percent

Step-by-step explanation:multiply 48 by .25 it will give you 12 which is the discount hope this helps god bless

Answer:

25%

Step-by-step explanation:

12/48=.25=25%

Answer: All of the answers are correct.

Step-by-step explanation:

A probability distribution is the collection of probabilities which defines the likelihood of observing all the various outcomes of an experiment or event. A probability distribution has two main properties which are that:

• Each probability in the distribution consist of a value between 0 and 1.

• The sum of all probabilities in the distribution equals 1.

Also, in probability, an outcome is the possible result of an experiment and each possible outcome gotten is unique, therefore the different outcomes are mutually exclusive i.e. only one outcome can occur on each trial during the experiment.

The sum of all probabilities of possible outcomes in a probability distribution must equal 1.0, and the probability of each outcome must be between 0.0 and 1.0, inclusive.

A probability distribution is a function that assigns probabilities to all possible outcomes of an experiment. The correct statement about a probability distribution is that the sum of all probabilities of possible outcomes must equal 1.0. This is known as the axiom of probability. In addition, the probabilities of each outcome must be between 0.0 and 1.0, inclusive. This ensures that probabilities are valid and within the appropriate range. The outcomes themselves do not have to be mutually exclusive; they can overlap or have common elements.

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Answer:

the first option ...-4

Step-by-step explanation:

The solution is Option A.

The value of the equation is x = -4

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = Negative 2 x + (negative 8) = 2 x + 8

Substituting the values in the equation , we get

( -2x ) + ( -8 ) = 2x + 8   be equation (1)

On simplifying the equation , we get

-2x - 8 = 2x + 8

Adding 8 on both sides of the equation , we get

2x + 16 = -2x

Adding 2x on both sides of the equation , we get

4x + 16 = 0

Subtracting 16 on both sides of the equation , we get

4x = -16

Divide by 4 on both sides of the equation , we get

x = -4

Therefore , the value of x is -4

Hence , the value of the equation is x = -4

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Answer: 32

Step-by-step explanation:

Use a fact family. 42 - 10 = 32.

You will get 32 as an answer.

So x = 32.

Answer:

32

Step-by-step explanation:

If x+10=42 then x=42-10 which makes x=32

Answer:

42

Step-by-step explanation:

If the shortest side is 7 and it is enlarged to be 24.5.

It is enlarged by a scale of 3.5.

so if you scale 12 by 3.5

then you get 42

Answer:

x=4.4

Step-by-step explanation:

expand the brackets

10x+15

full equation now

=x-23=10x+15-2 this makes it more simpler to find like terms

+2 on both sides

=x-25=10x+15

=+25 on both sides

x=10x+40

= -x on both sides

=9x=40

40/9=x

x=4.4

Answer:

[tex]x = - 4[/tex]

Step-by-step explanation:

[tex]x - 23 = 5(2x + 3) - 2 \\ x - 23 = 10x + 15 - 2 \\ - 23 - 15 + 2 = 10x - x \\ - 36 = 9x \\ \frac{ - 36}{9} = \frac{9x}{9} \\ - 4 = x[/tex]

Answer:

There is no answer to this, closest answer is the 1st choice

Step-by-step explanation:

Answer:2 identical side rectangle

2 identical end triangle

1 bottom rectangle

area of trialge=1/2bh

aera of rectangle=legnth tiems width

2 side rectangles are 5 by 10=50

times 2 since 2 of them 50*2=100

end triangles

1/2 times 8 times 3=12

2 of them

12 times 2=24

bottom

8 by 10

80

add everybody

100+24+80=204 in^2 i think this is how

Step-by-step explanation:

Answer:

2 identical side rectangle

2 identical end triangle

1 bottom rectangle

area of trialge=1/2bh

aera of rectangle=legnth tiems width

2 side rectangles are 5 by 10=50

times 2 since 2 of them 50*2=100

end triangles

1/2 times 8 times 3=12

2 of them

12 times 2=24

bottom

8 by 10

80

add everybody

100+24+80=204 in^2 i think this is how

Step-by-step explanation:

The option A mutual funds will be more effective.

Step-by-step explanation:

Option A:

Principal amount = $10000

Monthly deposit = $200

Time = 10 years

Rate of interest = 7%

Total deposit = (200 x 12 x 10) + 10000

= 24000 + 10000

= $34000

Interest = (34000 x 7 ) /100

= 340 x 7

= $2380

Total amount = 34000 + 2380

= $36380

Option B:

Principal amount = $10000

Monthly deposit = $200

Time = 5 years

Rate of interest = 9%

Total deposit = (200 x 12 x 5) + 10000

= 12000 + 10000

= $22000

Interest = (22000 x 9 ) /100

= $1980

Total amount = 22000+1980

= $23980

The option A mutual funds will be more effective.

Answer:

What is the difference in the final balances of the two mutual funds?

Step-by-step explanation:

The difference is $12,400.

Answer:

iiiiiiiiiiiiiiiiiiiiiiii believe its 8

Step-by-step explanation:

Answer:

729/64

Step-by-step explanation:

:)

Answer:

5 miles

Step-by-step explanation:

since she hopped in yards you must mulitiply both numbers 3520 and 5280 by 3 since there are three feet in a yard. then add together then divide the sum by 5280 since a mile is 5280 feet.

3520 X 3 = 10560

5280 X 3 = 15840

10560 + 15840 = 26400

26400/ 5280 = 5

Answer:

3x-2

Step-by-step explanation:

Answer:

3x-2

Step-by-step explanation:

"Less than" makes the whole expression changed.

If the less than was not there, it would have been 2-3x.

"Product" is multiplication. So it would be 3x.

The "Less than" also has less in it which is subtraction.

Answer:

The volume of the large box is 384 cubic units

Step-by-step explanation:

Here, we have;

The number of cubes along the base of the front of the large box (width) = 8 cubes

The number of cubes along the base of the side of the large box (length) = 8 cubes

The number of cubes along the right  side of the front of the large box (the box height)  = 6 cubes

The volume of the large box = Length × Width × Height

∴ The volume of the large box = 8 cubes × 8 cubes × 6 cubes = 384 cubic units.

The volume of the large box = 384 cubic units.

Answer:

[tex]\frac{225}{16} cm/s[/tex]

Step-by-step explanation:

We are given that

[tex]\frac{dV}{dt}=25cm^3/s[/tex]

Side of base=4 cm

l=w=4 cm

Height,h=12 cm

We have to find the rate at which the water level rising when the water level is 4 cm.

Volume of pyramid=[tex]\frac{1}{3}lwh=\frac{1}{3}l^2h[/tex]

[tex]\frac{l}{h}=\frac{4}{12}=\frac{1}{3}[/tex]

[tex]l=\frac{1}{3}h[/tex]

Substitute the value

[tex]V=\frac{1}{27}h^3[/tex]

Differentiate w.r.t t

[tex]\frac{dV}{dt}=\frac{3}{27}h^2\frac{dh}{dt}[/tex]

Substitute the values

[tex]25=\frac{1}{9}(4^2)\frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt}=\frac{25\times 9}{16}=\frac{225}{16} cm/s[/tex]

Final answer:

Using the volume of a pyramid and the concept of similar triangles, we set up a proportion to find the changing base area at a specific water level. Then, applying the product rule for differentiation, we relate the rate of volume change to the rate of height change, which allows us to solve for the water level rising rate when it is 4 cm.

Explanation:

To find the rate at which the water level is rising when the water level is 4 cm in an inverted pyramid being filled at a constant rate of 25 cubic centimeters per second, we can use the concept of similar triangles and the volume of a pyramid.

The volume V of a pyramid is given by V = (1/3)Bh, where B is the base area and h is the height. As the pyramid fills, the water forms a smaller, similar pyramid whose volume increases at a rate of 25 cm3/s.

Since the sides of the smaller pyramid are proportional to the height, we can set up a proportion using the side length s of the water level: s/4 = 4/12. Solving for s gives us s = 4 * (4/12) = 4/3 cm. The base area B of the water at this level is B = s2 = (4/3)2 cm2.

To find the rate of the rise of water dh/dt, we use the relation dV/dt = (1/3) * d(Bh)/dt. Since B is also changing with h, we have to use the product rule for differentiation: dV/dt = (1/3)(B(dh/dt) + h(dB/dt)). However, because B is a function of h2, dB/dt can be expressed as a function of dh/dt. This allows us to solve for dh/dt.