4, 16, 64, 256
4¹, 4², 4³, 4⁴
Do you see the pattern? [tex]a_{n} = 4^{n}[/tex]
Answer: D
Geoff has a bag that contains 4 red marbles and 6 blue marbles. He chooses two marbles at random and does not replace them. What is the probability that the first marble is blue and the second marble is red? A. B. C. D.
Answer: [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
First pick (blue) and Second pick (red)
[tex]\frac{6}{10}[/tex] x [tex]\frac{4}{9}[/tex]
= [tex]\frac{6(4)}{10(9)}[/tex]
= [tex]\frac{2(2)}{5(3)}[/tex]
= [tex]\frac{4}{15}[/tex]
Answer:
The answer is 4/15 hopefully this helps!
(04.05)Marcus spent 10 hours doing his homework last week. This week he spent 11 hours doing homework. He says that he spent 110% more time doing homework this week. Is he correct? Show your work to justify your decision.
Answer:
No
Step-by-step explanation:
11-10 = 1
He spent 1 hour more this week
Which is:
1/10 × 100 = 10% more
Marcus spent 10% more time doing homework this week. His calculation is wrong.
Time used last week by marcus = 10 hours
Time used this week by marcus = 11 hours
Difference in hours = 11 - 10 = 1 hour
This means that Marcus used 1 more hour this week than last week
% increase = 1/10 * 100
% increase = 10%
This shows that he spent 10% more time doing homework this week.
Learn more here: https://brainly.com/question/20710281
Write a real-world problem three yards of fabric will be cut into pieces so that each piece is 8 inches long.How many pieces can be cut?
Answer:
Stacy made a blanket using some fabric, she had 3 yards left over and decided to use the leftover pieces to make pot holders. She cut each piece into 8 inches long. Stacy had enough fabric to create 4.5 pieces.
Step-by-step explanation:
we find that 13 full pieces of fabric, each 8 inches long, can be cut from three yards of fabric.
The question asks how many pieces of fabric, each measuring 8 inches in length, can be cut from a total length of three yards of fabric. To begin with, we need to convert yards to inches, because the unit of measurement for the fabric pieces is in inches, not yards. We know that 1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches, hence 3 feet x 12 inches/foot = 36 inches). Therefore, three yards of fabric is 3 x 36 inches, which equals 108 inches.
Now, if each piece is to be 8 inches long, we divide the total number of inches by the length of one piece to find out how many pieces can be made:
108 inches / 8 inches/piece = 13.5 pieces.
However, since we cannot have half a piece of fabric, we can only make 13 full pieces, with a small remaining piece that would be less than 8 inches long.
Find the prime factorization of 210
A.) 2 X 3 X 5 X 7
B.) 2 X 3 X 35
C.) 2 X 7 X 15
To prime factorization would be A: 2 X 3 X 5 X 7
Because if your do 2 X 3 it would be 6
Then you do 5 X 7 it would be 35
And 6 X 35 would be 210
AND THAT IS FACTORING THE PROBLEM
[tex]210:2=105\\\\105:5=21\\\\21:3=7\\\\7:7=1\\\\210=2\cdot3\cdot5\cdot7[/tex]
What is the equation of the line with a slope of 3/4 that goes through the point (4,1) in slope-intercept form ?
The slope-point form of a line:
[tex]y-y_0=m(x-x_0)[/tex]
We have
[tex]m=\dfrac{3}{4}\\\\(4,\ 1)\to x_0=4,\ y_0=1[/tex]
Substitute:
[tex]y-1=\dfrac{3}{4}(x-4)[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
Solve for y:
[tex]y-1=\dfrac{3}{4}(x-4)\qquad|\text{use distributive property}\\\\y-1=\dfrac{3}{4}x-3\qquad|\text{add 1 to both sides}\\\\y=\dfrac{3}{4}x-2[/tex]
Answer: D.
For which values of x is the inequality 2(1 + x) > x + 8 true?
A) 3 & 2
B) 4 & 3
C) 6 & 5
D) 7 & 8
What is the solution of the equation when solved over the complex numbers? X2+24=0
The solution to the equation x² + 24 = 0 over the complex numbers is x = ±2√(6)i. After isolating x² on one side, we take the square root of both sides and introduce the imaginary unit i because the number under the square root is negative.
Explanation:To solve the equation x² + 24 = 0 over the complex numbers, we need to find values of x that satisfy the equation. This is a quadratic equation with 'a' as 1 (the coefficient of x²), 'b' as 0 (since there is no x term), and 'c' as 24.
We will first isolate x² by subtracting 24 from both sides of the equation:
x² = -24
Next, to find x, we take the square root of both sides. Remember that when we take the square root of a negative number, we get an imaginary number. The square root of -24 can be expressed as:
x = ±√(-24)
This simplifies to:
x = ±√(24) × ±i
Since √(24) is √(4 × 6), which simplifies to 2√(6), the final solution in terms of complex numbers is:
x = ±2√(6)i
If f(x) = 2x + 7 and g(x) = x2 2, what is [f o g](3)?
Answer:
The value [fog](3) is 29.
Step-by-step explanation:
The given functions are
[tex]f(x)=2x+7[/tex]
[tex]g(x)=x^2+2[/tex]
We have to find [fog](3).
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(3)=f(g(3))[/tex]
[tex](f\circ g)(3)=f(3^2+2)[/tex] [tex][\because g(x)=x^2+2][/tex]
[tex](f\circ g)(3)=f(11)[/tex]
[tex](f\circ g)(3)=2(11)+7[/tex] [tex][\because f(x)=2x+7][/tex]
[tex](f\circ g)(3)=22+7[/tex]
[tex](f\circ g)(3)=29[/tex]
Therefore the value [fog](3) is 29.
What needs to happen for the equation CH4 + O2 → CO2 + H2O to be balanced?
A. A coefficient of 2 must be added before both products.
B. A coefficient of 2 must be added before the second reactant and the second product.
C. Nothing, the equation is already balanced.
D. A coefficient of 2 must be added before both products and reactants.
Dreya is saving money to purchase a $900 computer, and she saves $10 the first week. Each week after that, she saves $3 more than the previous week, except in the last week, when she reaches $900. To have a final sum of excatly $900, how much money does dreya need to save in her final week of saving?
In the inequality, what are all the possible values of x? 2 − 3(2x + 1) < 6x(2 − 4) A) x ≥ 1 6 B) x ≤ 1 6 C) x ≥ − 1 6 D) x ≤ − 1 6
2 - 3(2x + 1) < 6x(2 - 4)
2 - 6x - 3 < 12x - 24x
-1 - 6x < -12x
-1 < -6x
Dividing by -6 both sides gives you;
1/6 < x or;
Final answer is x > 1/6
Answer:
A) x ≥ 1 6
: )
Last year a business had profits of $8,000.This year its profits are 5 times as great.This are this year's profits?
Find the slope of the line.
The slope:
[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]
Look at the picture.
6 units down → -6
2 units right → 2
[tex]m=\dfrac{-6}{2}=-3[/tex]
Answer: Slope = m = -3answer: [tex] \frac{3}{-1} x[/tex]
explanation:
slope-intercept formula ==> [tex]y = mx + b[/tex]
[tex]m[/tex] is slope , and [tex]b[/tex] is y-intercept
to find the slope you need to start at the y intercept and go 3 units up and 1 unit left. and if you repeat it again, until you reach the top of the graph and that would make partial of the line.
so, the slope is [tex]\frac{rise}{run}[/tex], so if you plug it in it would look like this
[tex]y = \frac{3}{-1} x + b[/tex]
A D D I T I O N A L I N F O
then you find the y-intercept which would be where the line intersects at the y axis, which is -10. plug the number into the equation
[tex]y = \frac{3}{-1} x - 10[/tex]
and that would make our final answer.
hope this helps! correct me if there is anything wrong ❤ from peachimin
Can someone please help me?
Which of the sets of ordered pairs represents a function?
A = {(2, −2), (5, −5), (−2, 2), (−5, 5)}
B = {(4, 2), (4, −2), (9, 3), (9, −3)}
Defined Terms:
Opposite rays form a:
point
ray
line
plane
Rays are always named with two points rays
he work shows how to use long division to find (x2 + 3x –9) ÷ (x – 2). What will be the remainder over the divisor?
Explanation of how to find the remainder using long division with a polynomial expression.
Explanation:Long Division Example:
We are given (x² + 3x – 9) ÷ (x – 2). To find the remainder using long division, we need to divide x² + 3x - 9 by x - 2 step by step.
Start by dividing x² by x, which gives x. Multiply x by (x - 2) to get x² - 2x.
Subtract x² - 2x from x² + 3x to get 5x. Bring down the -9.
Repeat the process: divide 5x by x to get 5. Multiply 5 by (x - 2) to get 5x - 10.
Subtract 5x - 10 from 5x - 9. The remainder is 1, which is the value over the divisor x - 2.
I'll Mark The First To Answer And Work Shown Brainliest!!!!!!!! PLEASE HELP ASAP
In 2005, there were 12,000 students at Beacon High. In 2010, there were 12,250. What is the rate of change in the number of students?
a. 250/yr
b. 50/yr
c. 42/yr
d. 200/yr
Answer:
Step-by-step explanation:
(2005, 12,000) (2005, 12,000)
x1 y1 x2 y2
m= (12,250-1200) / (2010-2005) = 250/5 = 50/1 = or 50
Girl works at a book store she gets $145 per week plus 5% for every book sold she wants to have $600 by the end of the week, how many books does she need to sell?
Sten had some apples in his basket. He ate 3 and then put 3 in each of 4 bags. How many apples did Sten start with in his basket?
3 * 4 + 3 = 12 + 3 = 15
Answer: He had 15 apples.
Find f(6) if f(x) = x2 ÷ 3 + x.
4
10
18
f(x) = x2 ÷ 3 + x
f(6)
Replace X with 6 then follow order of operations.
6^2 / 3 + 6
6^2 = 36:
36 / 3 + 6
36 /3 = 12:
Add:
12 + 6 = 18
The answer is 18
What roles did African American men take on during the war? Check all of the boxes that apply They worked as cooks. They enlisted in the Union Army. They served as generals in the army.
All except generals
Union supported African Americans as soldiers
They worked as slaves so obviously cooks
Answer:
They worked as cooks.They enlisted in the Union Army.Step-by-step explanation:
The emancipation proclamation allowed the African American men to serve in the Union army.
They worked as cooks. Enslaved blacks were sometimes used for camp labor also.
But they did not served as generals in the army.
Hence, the answer is :
They worked as cooks.They enlisted in the Union Army.A person travels to a destination at a rate of 50m/h and returns the next day at a rate of 40m/h. If the time returning is 1hour more than the time going, how many miles are traveled in all?
the time returning=x h,
the time going=(x-1) h,
s=t*v
s=(x-1)*50,
s=x*40,
(x-1)*50=x*40
x=5h,
s=t*v=5*50=250 miles
PLEASE HELP! The high school band wants to sell two types of cookies, chocolate chip and peanut butter, as a fundraiser. A dozen chocolate chip cookies requires 2 cups of flour and 1 egg. A dozen peanut butter cookies uses 3 cups of flour and 4 eggs. The club has 90 cups of flour and 80 eggs on hand. The profit on the chocolate chip cookies is $1 per dozen and on the peanut butter is $1.50 per dozen. If they want to offer both types of cookies, how many of each cookie should the club make to maximize profits?
a.
infeasible solutions
c.
24 dozen chocolate chip
14 dozen peanut butter
b.
30 dozen chocolate chip
25 dozen peanut butter
d.
20 dozen chocolate chip
18 dozen peanut butter
Answer:
24 dozen chocolate chip
14 dozen peanut butter
Step-by-step explanation:
x = number of dozen chocolate chip cookies
y = number of dozen peanut butter cookies
Total number of cups of flour is:
2x + 3y ≤ 90
Total number of eggs is:
x + 4y ≤ 80
Total profit is:
P = x + 1.5y
Since this is multiple choice, one method would be to calculate the profit for each option, then choose the one that's largest.
But let's try solving this algebraically. x and y are positive integers, and we want them to be as large as possible.
Let's start by assuming the solution is on the line 2x + 3y = 90.
x + 4y ≤ 80
2x + 8y ≤ 160
90 − 3y + 8y ≤ 160
5y ≤ 70
y ≤ 14
If y = 14, x = 24, and P = 45.
Now let's assume the solution is on the line x + 4y = 80.
2x + 3y ≤ 90
2 (80 − 4y) + 3y ≤ 90
160 − 8y + 3y ≤ 90
70 ≤ 5y
14 ≤ y
Therefore, to maximize the profit, they should bake 24 dozen chocolate chip cookies and 14 dozen peanut butter cookies.
Find r if (r, 6) and (5, -4) are two points on a line with a slope of 5/7 (Hint: use the slope formula)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex](r,\ 6),\ (5,\ -4)\\\\m=\dfrac{5}{7}[/tex]
Substitute
[tex]\dfrac{-4-6}{5-r}=\dfrac{5}{7}\\\\\dfrac{-10}{5-r}=\dfrac{5}{7}\qquad|\text{cross multiply}\\\\5(5-r)=(-10)(7)\qquad|\text{use distributive property}\\\\25-5r=-70\qquad|-25\\\\-5r=-95\qquad|:(-5)\\\\\boxed{r=19}[/tex]
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Which of the following equations represents the line with a slope of negative 8/7 and a y-intercept of negative 3?
y = 8/7x - 3
y = 8/7x + 3
y = -8/7x - 3
y = -8/7x + 3
Answer:
y = -8/7x - 3
Step-by-step explanation:
A line represents a linear relationship between x and y with constant slope and defined for all values of x and y.
Any line equation in slope intercept form would be of the form
y =mx+c where
m = slope of line
and c = y intercept
In our quesion we are given that slope of line = -8/7
and intercept = negative 3 = -3
Hence equation is
y =-8x/7-3
item 10 question 1 identify the percent of change as an increase or a decrease. 5/4 to 3/8
[tex]\frac{(new) - (original)}{original} = \frac{\frac{3}{8}- \frac{5}{4} }{\frac{5}{4} }[/tex]
[tex]\frac{3}{8} - \frac{5}{4} (\frac{2}{2}) = \frac{3}{8} - \frac{10}{8} = \frac{-7}{8}[/tex]
[tex]\frac{-7}{8}[/tex] ÷ [tex]\frac{5}{4}[/tex]
= [tex]\frac{-7}{8}[/tex] * [tex]\frac{4}{5}[/tex]
= [tex]\frac{-7(4)}{8(5)}[/tex]
= [tex]\frac{-7}{2(5)}[/tex]
= [tex]\frac{-7}{10}[/tex]
= -0.70
multiply by 100 to get the percent: - 70% (the negative represents decrease)
Answer: 70% decrease
Which integer is closest to 0 on the number line?
A.
–12
B.
–8
C.
10
D.
14
An integer is close to zero if it is "small".
By small, we mean that it is small in absolute value. In fact, for any given distance [tex] d [/tex], there are two integers that are [tex] d [/tex] units away from zero: [tex]d [/tex] and [tex] -d [/tex].
So, for example, -6 is close to zero than 8, because -6 is six units away from zero, while 8 is eight units away from zero.
So, the answer is B, -8, because it is 8 units away from zero. The other options A, C and D are, respectively, 12, 10 and 14 units away from zero.
To make fruit salad sara uses 28 ounces of pineapple 21 ounces of apples 19 ounces of bannas and 16onces of mango how many 6-ounce serving of fruit salaf can sarah make?
please help asap 30 pts
[tex]-18-5y\geq52\qquad|\text{add 18 to both sides}\\\\-5y\geq70\qquad|\text{change the signs}\\\\5y\leq-70\qquad|\text{divide both sides by 5}\\\\y\leq-14\\\\Answer:\ \boxed{d.\ y\leq-14}[/tex]