simplify the expression below. (-3x2 + 2x - 4) + (4x2 + 5x +9)

Answer:

-5/4; -4/3

Step-by-step explanation:

12x^2 + 31x + 20 =

(4x + 5)(3x + 4) -->

x = -5/4 OR -4/3

We have been given that in the morning an iceberg weighed 380,000 pounds. It lost 0.3% of its weight during the day. We are asked to find the weight of the ice-berg at the end of the day.

The weight of the ice-berg at the end of the day would be original weight of ice-berg minus 0.3% of original weight.

[tex]\text{The weight of the ice-berg at the end of the day}=380,000-380,000\times \frac{0.3}{100}[/tex]

[tex]\text{The weight of the ice-berg at the end of the day}=380,000-3800\times 0.3[/tex]

[tex]\text{The weight of the ice-berg at the end of the day}=380,000-1140[/tex]

[tex]\text{The weight of the ice-berg at the end of the day}=378,860[/tex]

Therefore, the weight of the ice-berg at the end of the day would be 378,860 pounds.

Answer:

378860 pounds

Step-by-step explanation:

Answer: The Sun is the major source of energy for organisms and the ecosystems of which they are a part. Producers such as plants, algae, and cyanobacteria use the energy from sunlight to make organic matter from carbon dioxide and water. This establishes the beginning of energy flow through almost all food webs.

ANSWER: The statistical procedure that should be performed is REGRESSION.

Step-by-step explanation: Regression is a statistical procedure that is used to estimate the relationship between an independent variable and a dependent variable using their mean values.

The independent variable in this case is the hours each student spend in studying, while the dependent variable is the students grade.

Since the researcher wants to determine if the hours a student spend in studying maths and science has any significant effect on their grades. The researcher should use regression, because it will show if the two variables are related and how it relates, by showing how far the points are from the trend lines of the graph.

Answer:

It will take 36.1 years for her money to reach $105,000.

Step-by-step explanation:

The amount of money earned after t years in continuous interest is given by:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial investment and r is the interest rate, as a decimal.

Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%.

This means that [tex]P(0) = 7000, r = 0.075[/tex]

How long will it take for her money to reach $105,000?

This is t for which P(t) = 105000.

[tex]P(t) = P(0)e^{rt}[/tex]

[tex]105000 = 7000e^{0.075t}[/tex]

[tex]e^{0.075t} = \frac{105000}{7000}[/tex]

[tex]e^{0.075t} = 15[/tex]

[tex]\ln{e^{0.075t}} = \ln{15}[/tex]

[tex]0.075t = \ln{15}[/tex]

[tex]t = \frac{\ln{15}}{0.075}[/tex]

[tex]t = 36.1[/tex]

It will take 36.1 years for her money to reach $105,000.

Answer:

(a) Is not possible

(b) It is possible

(c) It is possible

(d) Is NOT possible.

Step-by-step explanation:

(a)

Is not possible, notice that for any function [tex]g[/tex]  such that

[tex]g : \mathbb{R} \rightarrow \mathbb{R}[/tex]

you would have that

[tex](g\circ f)(x) = g(f(x)) = g(|x|)[/tex]

And for, lets say -3,3 you have that

[tex]g(|-3|) = g(|3|) = g(3)[/tex] therefore is not possible to find a function that is one to one.

(b)

It is possible. Take the following function

[tex]g(x) = x\sin(x)[/tex] since [tex]\sin[/tex] is periodic it will take positive and negative numbers and if you multiply by [tex]x[/tex] each period will become bigger and bigger.

(c)

It is possible. Take the function

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

Then

[tex](f \circ g )(x) = | \sqrt{x} | = \sqrt{x}[/tex]    and [tex]\sqrt{x}[/tex] is one to one.

(d)

It is NOT possible because   [tex](f\circ g)(x) = f(g(x)) = |g(x)|[/tex] and that will always be positive.  

Answer:

C

Step-by-step explanation:

A. 558 m2

B. 976 m2

C. 1,680 m2

D. 1,750 m2

Answer:

1064.64

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Because their slopes are equal. Rest of the step-by-step explanation is in the attached file!!

Final answer:

To calculate the probability that both a seventh grader and an eighth grader selected at random are girls, multiply the probability of selecting a girl from each grade. For the seventh grade, it's 1/4, and for the eighth grade, it's 7/10. The overall probability of both being girls is therefore 7/40.

Explanation:

The question involves determining the probability that both students selected for a competition from different grades are girls. To find this, we need to consider the number of girls in each of the two grades separately.

In the seventh grade, there are 3 girls out of 12 students. So, the probability of selecting a girl from the seventh grade is 3/12, which simplifies to 1/4. In the eighth grade, there are 7 girls out of 10 students. Therefore, the probability of selecting a girl from the eighth grade is 7/10.

To find the overall probability of selecting girls from both grades, we multiply the probabilities of each event since they are independent: (1/4) * (7/10) = 7/40.

Thus, the probability that both selected students are girls is 7/40.

We have been given a graph. We are asked to find the values of x,y and z.

We will use parallel line's angles to solve our given problem.

We know that corresponding angles of parallel lines are equal.

We can see that angle [tex]2x+3[/tex] and 67 are corresponding angles, so we can set an equation as:

[tex]2x+3=67[/tex]

[tex]2x+3-3=67-3[/tex]

[tex]2x=64[/tex]

[tex]\frac{2x}{2}=\frac{64}{2}[/tex]

[tex]x=32[/tex]  

Therefore, the value of x is 32.

We know that interior angles on same side of transversal are supplementary.

We can see that [tex]3y+5[/tex] and 67 are interior angles, so we can set an equation as:

[tex]3y+5=67[/tex]

[tex]3y+5-5=67-5[/tex]

[tex]3y=62[/tex]

[tex]\frac{3y}{3}=\frac{62}{3}[/tex]

[tex]y=\frac{62}{3}[/tex]

Therefore, the value of y is [tex]\frac{62}{3}[/tex].

We can set an equation for angle z as:

[tex]4z+13=2x+3[/tex]

[tex]4z+13-13=2x+3-13[/tex]

[tex]4z=2x-10[/tex]

Upon substituting value of z, we will get:

[tex]4z=2(32)-10[/tex]

[tex]4z=64-10[/tex]

[tex]4z=54[/tex]

[tex]\frac{4z}{4}=\frac{54}{4}[/tex]

[tex]z=13.5[/tex]

Therefore, the value of z is 13.5.

Answer:

4/5 (not drawing a black marble)

3/10 (drawing a red marble)

Step-by-step explanation:

Answer:

40 miles

Step-by-step explanation:

Let's set x to the number of miles driven, and t to the number of hours it took to drive.

We know that 40t is equal to x.

We also know that 40t is equal to 30(t + 1/3).

Solve for t:

40t = 30(t+1/3)

40t = 30t + 10

Subtract 30t from both sides:

10t = 10

Divide 10 from both sides:

t = 1

40t = 40 x 1 = 40 miles

I drove 40 miles.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.

Suppose, I drove n number of miles and it took me x time in hours.

We know that 40x is equal to n.

Since it would take 20 more minutes, so we have the division of 20/60 = 1/3

Then, 40x is equal to 30(x+ 1/3).

Solve for t:

40x = 30(x+1/3)

40x = 30x + 10

10x = 10

Now , divide by 10 on both sides,

x = 1

40x = 40 x 1 = 40 miles

Therefore, I drove 40 miles.

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Answer:

Yes because 10 times 8 is 80.

Step-by-step explanation:

Answer: 80 IS a multiple of 10 because 8 times 10 is 80.

Step-by-step explanation:

Answer:

9 boards

Step-by-step explanation:

2/3 of the porch= 6 boards

so to figure out how much one third of the porch needs you find half of what it takes to fill in 2/3 of the porch and you get 3.

so 3=1/3 of the porch

then you simply do 3times 3 or 3+3+3 and you get 9

so it takes 9 boards to fill the whole porch

Answer:

The number of candies in the sixth jar is 42.

Step-by-step explanation:

Assume that there are x number of candies in each of the six jars.

⇒ After Alice moves half of the candies from the first jar to the second jar, the number of candies in the second jar is:

[tex]\text{Number of candies in the 2nd jar}=x+\fracx}{2}=\frac{3}{2}x[/tex]

⇒ After Boris moves half of the candies from the second jar to the third jar, the number of candies in the third jar is:

[tex]\text{Number of candies in the 3rd jar}=x+\frac{3x}{4}=\frac{7}{4}x[/tex]

⇒ After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the fourth jar is:

[tex]\text{Number of candies in the 4th jar}=x+\frac{7x}{4}=\frac{15}{8}x[/tex]

⇒ After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fifth jar is:

[tex]\text{Number of candies in the 5th jar}=x+\frac{15x}{16}=\frac{31}{16}x[/tex]

⇒ After Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the sixth jar is:

[tex]\text{Number of candies in the 6th jar}=x+\frac{31x}{32}=\frac{63}{32}x[/tex]

Now, it is provided that at the end, 30 candies are in the fourth jar.

Compute the value of x as follows:

[tex]\text{Number of candies in the 4th jar}=40\\\\\frac{15}{8}x=40\\\\x=\frac{40\times 8}{15}\\\\x=\frac{64}{3}[/tex]

Compute the number of candies in the sixth jar as follows:

[tex]\text{Number of candies in the 6th jar}=\frac{63}{32}x\\[/tex]

                                                    [tex]=\frac{63}{32}\times\frac{64}{3}\\\\=21\times2\\\\=42[/tex]

Thus, the number of candies in the sixth jar is 42.

There are now 33.75  candies in the sixth jar.

Let's denote:

-  x  as the initial number of candies in each jar.

After Alice moves half of the candies from the first jar to the second jar, the number of candies in the first jar becomes [tex]\( \frac{x}{2} \)[/tex], and the number of candies in the second jar becomes [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .

After Boris moves half of the candies from the second jar to the third jar, the number of candies in the second jar becomes [tex]\( \frac{3x}{4} \)[/tex], and the number of candies in the third jar becomes  [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .

After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the third jar becomes [tex]\( \frac{x}{2} \)[/tex], and the number of candies in the fourth jar becomes  [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .

After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fourth jar becomes  [tex]\( \frac{3x}{4} \)[/tex], and the number of candies in the fifth jar becomes [tex]\( \frac{3x}{4} + \frac{3x}{8} = \frac{9x}{8} \).[/tex]

Finally, after Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the fifth jar becomes [tex]\( \frac{9x}{16} \)[/tex], and the number of candies in the sixth jar becomes [tex]\( \frac{9x}{16} + \frac{9x}{32} = \frac{27x}{32} \).[/tex]

Given that 30 candies are now in the fourth jar, we can set up the equation:

[tex]\[ \frac{3x}{4} = 30 \][/tex]

Solving for  x :

[tex]\[ x = \frac{4 \times 30}{3} = 40 \][/tex]

Now, we can find the number of candies in the sixth jar:

[tex]\[ \frac{27 \times 40}{32} = \frac{1080}{32} = 33.75 \][/tex]

So, there are now 33.75  candies in the sixth jar.

Answer:

V=lwh /3

Step-by-step explanation:

Answer:

a. V=1/3(12)(8)(10)

Step-by-step explanation:

Answer:

$19.99

Step-by-step explanation:

Take the price for 2 pairs and divide by 2 to get the price for one pair

39.98 /2

19.99 for one pair

Answer: The new drawing would be larger than the first drawing.

Step-by-step explanation:

A scale factor greater that one is an enlargement, but one smaller than one is a reduction

The second drawing will be 5 times bigger than the first one.

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

The scale factor is done due to the unpractical measurement of any figure.

Given in the first drawing scale factor is 1:60

So Andre takes 60 units as 1

For example, it is 60 inches to 1 inch.

In the second drawing, Andre took 1:12

So he took 12 units as 1

For example 12 inches to 1

Now multiply by 5 then 5:60

So 60 inches to 5 inches means the second drawing is 5 times bigger the first one.

Hence "The second drawing will be 5 times bigger than the first one".

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Answer:6.3

Step-by-step explanation: 6.8 +1.5 -1.2 -0.8=6.3

The amount of flour left is 6.3 kg.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total flour = 6.8 + 1.5 = 8.3 kg

Amount of flour used = 1.2 + 0.8 = 2 kg

The amount of flour left.

= 8.3 - 2

= 6.3 kg

Thus,

6.3 kg of flour is left.

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Teh value of x is 23° (D)

Step-by-step explanation:

Total of angel = 360°

The value of x :

(2x + 15)° + 119° + 99° + 81° = 360°

2x + (15 + 119 + 99 + 81)° = 360°

2x + 314° = 360°

2x = 360° - 314°

2x = 46

x = 46 ÷ 2

x = 23°

So, the value of x is 23° (D)

Hope it helpful and useful :)

Answer:

  0.56 mg

Step-by-step explanation:

Put 6 where t is and do the arithmetic.

  M(6) = 50(e^(-0.75·6)) = 50e^-4.5 ≈ 0.56

Olivia will have about 0.56 mg of medication remaining in her blood.

Jordan's total tax due, using the provided tax brackets and rates, is $4,009.50.

To compute Jordan's total tax due, we need to apply the marginal tax rates to each income bracket. Here's the breakdown for Jordan's taxable income of $35,000:

1. Income up to $9,525: Tax rate 10%

  Tax on this bracket = $9,525 * 0.10 = $952.50

2. Income from $9,526 to $38,700: Tax rate 12%

  Taxable income in this bracket = $35,000 - $9,525 = $25,475

  Tax on this bracket = $25,475 * 0.12 = $3,057

Now, add the taxes from each bracket to find the total tax due:

Total tax due = Tax on the first bracket + Tax on the second bracket

             = $952.50 + $3,057

             = $4,009.50

Therefore, Jordan's total tax due, using the provided tax brackets and rates, is $4,009.50.

The probable question may be:

"Jordan is a single taxpayer with a taxable income of $35,000. Using the provided tax bracket table for single taxpayers, where different tax rates apply to specific income brackets, compute Jordan's total tax due. The tax rates for the respective income brackets are as follows: 10% for income up to $9,525, 12% for income between $9,526 and $38,700. Please calculate Jordan's total tax due using the marginal tax rates."

Jordan's total tax due is $4,009.48. To calculate this, we determine the tax for each income bracket Jordan falls into and add them together. Jordan's taxable income of $35,000 falls into the 12% tax bracket, so we use the 12% tax rate to calculate the tax due in that bracket. We also calculate the tax due in the 10% tax bracket for the remaining income.

To find Jordan's total tax due, we need to determine which income bracket he falls into and calculate the tax for each bracket using the corresponding tax rate. Jordan has a taxable income of $35,000, which falls into the 12% tax bracket. So, we will use the tax rate of 12% to calculate his tax due.

Step 1: Calculate the tax on the income that falls in the 12% tax bracket:

So, Jordan's tax due for the 12% tax bracket is $3,056.88.

Step 2: Calculate the tax on the income that falls in the 10% tax bracket:

So, Jordan's tax due for the 10% tax bracket is $952.60.

Step 3: Add the tax due for each bracket to get Jordan's total tax due:

Total tax due = $3,056.88 + $952.60 = $4,009.48.

Answer:

The answer is digit

Step-by-step explanation:

A single number between 0 and 9 is a digit, which often makes up larger numbers.

Answer:

86.64% probability that the resulting sample proportion is within .02 of the true proportion.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

For the sampling distribution of a sample proportion p in a sample of size n, we have that [tex]\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this problem:

[tex]\mu = 0.2, \sigma = \sqrt{\frac{0.2*0.8}{900}} = 0.0133[/tex]

How likely is the resulting sample proportion to be within .02 of the true proportion (i.e., between .18 and .22)?

This is the pvalue of Z when X = 0.22 subtracted by the pvalue of Z when X = 0.18.

X = 0.22

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.22 - 0.2}{0.0133}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a pvalue of 0.9332.

X = 0.18

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.18 - 0.2}{0.0133}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

0.9332 - 0.0668 = 0.8664

86.64% probability that the resulting sample proportion is within .02 of the true proportion.

Answer:

(A)One-third(36)(7)= 84 cubic units

Step-by-step explanation:

Volume of a Pyramid = [tex]\frac{1}{3}X$Base Area X Height[/tex]

The base is a rectangle

Base Area = 9 X 4=36 Square Units

Height =7 Units

Therefore:

Volume  [tex]=\frac{1}{3}(36)(7)[/tex]

=84 Cubic Units

Answer:

Step-by-step explanation:

Answer:

RT ≈ 7.82

Step-by-step explanation:

tan θ = opposite / adjacent

tan 41 = RT / 8

RT = tan 41 × 8

RT = 0.869 × 8

RT = 7.821

RT ≈ 7.82

Answer:

Alisha

Step-by-step explanation:

Speeds:

Bill:

315/7 = 45 mph

Alisha:

235/5 = 47 mph

Joanna:

414/9 = 46 mph

Answer:

The answer is Alisha.

Step-by-step explanation:

235 mph divided by 5 is equal to 47 mph.

Answer:

a) Predicted value =0.5×18+6= 15

b) Predicted value =0.5×15+6= 13.5

c) Since least square equation has the tendency to regress the outcome toward mean value , as both the explanatory variable (in part a and b) are above mean value , the response variable are smaller then them.

Step-by-step explanation:

[ Find the attachments for explanation]

Final answer:

Explaining how to predict the educational level of a spouse based on correlation, and discussing why well-educated individuals may marry partners with different education levels.

Explanation:

The questions can be answered as -

(a) Predicting the educational level of a woman whose husband has completed 18 years of schooling:

Given that the correlation between the educational levels of husbands and wives is 0.50, we can use this correlation to predict the wife's educational level.

Educational level of wife = correlation * (wife's SD / husband's SD) * husband's years of schooling + wife's average years of schooling.

(b) Predicting the educational level of a man whose wife has completed 15 years of schooling:

Apply the same formula as in (a) but with the wife's years of schooling given as 15 years.

(c) Explanation of why well-educated men marry women less educated than themselves:

This can occur due to various factors such as social dynamics, career aspirations, or personal preferences.

Answer:

Juan has 35 orders

Step-by-step explanation:

you subtract 40 from 75 to get 35

Juan has 35 cookie dough orders for the school fundraiser

The question involves solving a simple algebra problem related to a school fundraiser involving cookie dough orders. Juan and Rob have a total of 75 cookie dough orders together. Juan has t orders and Rob has 40 orders. The problem can be represented by the equation t + 40 = 75. To find out how many cookie dough orders Juan has, we subtract 40 from both sides of the equation, which gives us t = 35. So, Juan has 35 cookie dough orders.

Final answer:

Four possible solutions to the inequality X > -1 are 0, 1, 2, and 2.5, as each of these values is greater than -1. The solution set in interval notation is (-1, ∞).

Explanation:

The inequality in question is X > -1. To provide four possible solutions, we are essentially looking for any four numbers that are greater than -1. Remember, there are an infinite number of solutions since X can be any value greater than -1, but here are four specific examples:

Each of these values satisfies the inequality X > -1, because they are all greater than -1. It is important to note that solutions to inequalities like this one are often represented in interval notation, in this case, it would be (-1, ∞), meaning any number greater than -1 but less than infinity.