The general formula of an arithmetic sequence is:
[tex]a_n=a_1+(n-1)\cdot d[/tex]Where d is known as the common difference and it represents the distance between consecutive terms of the sequence. So we can calculate this distance for each of the four options:
[tex]\begin{gathered} 768,192,48,12,3 \\ 768-192=576 \\ 192-48=144 \end{gathered}[/tex]So in the first sequence the difference between terms is not even constant so this is not the correct option.
[tex]\begin{gathered} 31-35=-4 \\ 27-31=-4 \\ 23-27=-4 \\ 19-23=-4 \end{gathered}[/tex]In the second sequence the distance is -4 so this is a possible answer.
[tex]\begin{gathered} 20-24=-4 \\ 16-20=-4 \\ 4-16=-12 \\ 0-4=-4 \end{gathered}[/tex]In the third sequence the distance is not always the same so we can discard this option.
[tex]\begin{gathered} -20-5=-25 \\ 80-(-20)=100 \end{gathered}[/tex]Here the distance isn't constant so the fourth option can also be discarded.
Then the only sequence with a distance d=-4 is the second option.
if ZQPS is a right angle and mLQPR = 71 ° . what is mZRPS
Step 1:
A right angle is 90 degree
Step 2:
angle
angle
angle
Step 3:
Sum of angle QPR and RPS = 90 i.e right angle
angle RPS = 90 - 71
m
Rewrite each of the following expressions so that they have no division
Using the law of indices,
[tex]\frac{1}{x^6}[/tex]will be
[tex]\frac{1}{x^6}=x^{-6}[/tex]solve and graph the following inequality: x + 19 > 31
You have the following inequality:
x + 19 > 31
subtract 19 both sides and simplify:
x > 31 - 19
x > 12
The graph of the previous inequality is:
Given the function f(x) = 2x2 - 5x + 1. Calculate the following values: f(-2) = f(-1) = f(0) = f(1) = f(2) Question Hon
Given function is
[tex]f(x)=2x^2-5x+1[/tex]Substitute the value of -2 in the equation we get
[tex]\begin{gathered} f(-2)=2(-2)^2-5\times-2+1_{} \\ =8+10+1 \\ =19 \end{gathered}[/tex]Similarly find other values
[tex]\begin{gathered} f(-1)=2(-1)^2-5\times-1+1_{} \\ =2+5+1 \\ =8 \end{gathered}[/tex]And then similarly f(1)=-2 and f(2)=-1 and f(0)=1
[tex]\begin{gathered} f(0)=2(0)^2-5\times0+1_{} \\ =0+0+1 \\ =1 \end{gathered}[/tex][tex]\begin{gathered} f(0)=2(0)^2-5\times0+1_{} \\ =0+0+1 \\ =1 \end{gathered}[/tex]You have $10,000 in a savings account. You want to take most of the money out and invest it in stocks and bonds. You decide to invest nine times as much as you leave in the account. You also decide to invest five times as much in stocks as in bonds. How much will you invest in stocks, how much in bonds, and how much will youleave in savings?
Answer:
7,500 in stocks
1,500 in bonds
1,000 in savings
Explanation:
First, let's call x the quantity that you will leave in saving and y the quantity that you will invest in stocks and z the quantity that you will invest in bonds.
Now, we can formulate the following equations:
x + y + z = 10,000
y + z = 9x
y = 5z
Because you have 10,000 in savings, you decide to invest nine times as much as you leave in the account, and you also decide to invest five times as much in stocks as in bonds.
So, we can rewrite the expressions as:
x + y + z = 10,000
-9x + y + z = 0
y - 5z = 0
Now, we can multiply the second equation by -1 and sum this equation with the first one as:
-9x + y + z = 0
(-9x + y + z)*(-1) = 0*(-1)
9x - y - z = 0
Then, the sum is equal to:
x + y + z = 10,000
9x - y - z = 0
10x - 0 - 0 = 10,000
10x = 10,000
x = 10,000/10
x = 1,000
Replacing x on the second equation, we get:
9x - y - z = 0
9*1,000 - y - z = 0
9,000 - y - z = 0
-y - z = - 9,000
Now, we can add the equation with the third one as:
-y - z = - 9,000
y - 5z = 0
0 - 6z = -9,000
-6z = -9000
z = -9000/(-6)
z = 1,500
Finally, using the third equation, the value of y is equal to:
y = 5z
y = 5*1500
y = 7,500
Therefore, you will invest 7,500 in stocks, 1,500 in bonds and you will leave 1,000 in savings.
19. If the cost price of 18 apples is the same as selling price of 16 apples, what is the profit in $ as well as percentage gain?
Answer
Percent Gain = 12.5%
Explanation
We are told that the
cost price of 18 apples = selling price of 16 apples
Let the cost price of an apple be x dollars
Let the selling price of an apple be y dollars
Buying 18 apples will cost 18 × x = (18x) dollars
Selling 16 apples will bring in 16 × y = (16y) dollars
Recall,
cost price of 18 apples = selling price of 16 apples
18x = 16y
We can rewrite as
16y = 18x
Divide both sides by 16
(16y/16) = (18x/16)
y = 1.125x
Percent gain is calculated as
[tex]\text{Percent Gain = }\frac{(\text{Selling price)-(Cost price)}}{Cost\text{ price}}\times100\text{ percent}[/tex]Selling price = y
Cost price = x
But recall that
y = 1.125x
[tex]\begin{gathered} \text{Percent Gain = }\frac{y-x}{x}\times100\text{ percent} \\ =\frac{1.125x-x}{x}\times100\text{ percent} \\ =\frac{0.125x}{x}\times100\text{ percent} \\ =0.125\times100\text{ percent} \\ =12.5\text{ percent} \end{gathered}[/tex]Hope this Helps!!!
What is the volume of the following prism?this is a prism with a right triangle as the base. The width of the triangle is 8 inches and the height of the triangle is 8 inches. The height of the prism is 12 inches.A. 768 m³B. 150 m³C. 384 m³D. 374 m³
Given the following information
Volume of the prism=?
base of the prism= right triangle
volume of a prism with a right triangle as a base is given by
[tex]\frac{1}{2}*b*a*h[/tex]where
b= base of the triangle = 8
a= height of the triangle = 8
h= height of the prism=12
[tex]V=\frac{1}{2}8*8*12[/tex][tex]V=\frac{768}{2}[/tex][tex]V=384m^3[/tex]36 unless for feeling nice to answer the 3 of them
36.
y=3x+2
f(x) can replace y
the answer is y
what is the pi of 53/17
One way to calculate pi is by dividing the circunferemce by the diameter. So you just need to calculate the ratio 53/17. Using a calculator you get that
[tex]\frac{53}{17}=3.11764[/tex]Shelley has a bag containing three balls: one red, one yellow, and one green. All balls are equally likely to be chosen. Shelley will choose one ball without looking in the bag. What is the probability that Shelley will choose the yellow ball out of the bag? A. 2/3 B. 3/1 C. 3/3 D. 1/3
Answer:
D. 1/3
Explanation:
In the bag, there are one red, one yellow, and one green ball.
Number of yellow ball = 1
Total number of balls = 3
Thus, the probability that Shelley will choose the yellow ball out of the bag:
[tex]=\frac{1}{3}[/tex]T
Answer: D
Step-by-step explanation: There is 3 balls, lets say that is 3/3, and a yellow ball is 1, which is 1/3
Evaluate 2(x-1), if x= -3
To evaluate the expression for x = -3, we simply put in -3 whereever we see x in the expression.
Doing this gives us
[tex]2(x-1)\rightarrow2(-3-1)[/tex]We now simplify the expression on the right
[tex]=2(-4)[/tex][tex]=-8[/tex]which is our answer!
12. Make an estimate and then divide as if the dividend was a whole number. Use the estimate to place your decimal.8.46 ➗3=Estimate: What partial quotients did you use? ___how to divide 3 into 8.46 dividing decimals?______________________Answer:
Given data:
The given expression is 8.46 ➗3.
The given expression can be written as,
Thus, the quotient is 2.82 which is in decimal.
in an election being held by the associated students organization, there are eight candidates for president, five for five president, five for secretary, and seven for treasurer. How many different possible outcomes are there for this election?
we have
eight candidates for president
five for secretary
seven for treasurer
therefore
The different possible outcomes is giving by
(8)*(5)*(7)=280 outcomes
the answer is 280 outcomesRewrite the division problem into a multiplication problem 1/4 ÷ 3/5
ANSWER
[tex]\text{ }\frac{1}{4}\cdot\text{ }\frac{5}{3}[/tex]EXPLANATION
We want to rewrite the division problem into a multiplication one.
To do this, we have to change the division sign to a multiplication sign, and then, we invert the fraction on the right.
That is:
[tex]\begin{gathered} \frac{1}{4}\div\frac{3}{5} \\ \Rightarrow\text{ }\frac{1}{4}\cdot\text{ }\frac{5}{3} \end{gathered}[/tex]That is the answer.
Find the slope-intercept form of the line that satisfies the given conditions.x-intercept 8, y-intercept −3
Given:
A line satisfies the given conditions.
x-intercept 8, y-intercept −3
The x-intercept is the value of x when y = 0
The y-intercept is the value of y when x = 0
So, the given line passes through the points (8, 0) and (0, -3)
We will find the slope using the following formula:
[tex]$$slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]Substitute with points:
[tex]m=\frac{-3-0}{0-8}=\frac{-3}{-8}=\frac{3}{8}[/tex]The slope-intercept form is: y = m * x + b
substitute m = 3/8 and b = -3
So, the answer will be, that the equation of the line is as follows:
[tex]y=\frac{3}{8}x-3[/tex]Convert: 9 kilogramsmilligrams
Answer
9,000,000 milligrams
Step-by-step explanation
1 kilogram is equivalent to 1,000,000 milligrams. Using this conversion factor, the equivalence of 9 kilograms is found as follows:
[tex]\begin{gathered} 9\text{ kg }=9\text{ kg}{}\cdot\frac{1,000,000\text{ mg}}{1\text{ kg}} \\ \text{ SImplifying the units:} \\ 9\text{ kg }=9\cdot1,000,000\text{ mg} \\ 9\text{ kg}=9,000,000\text{ mg} \end{gathered}[/tex]Margaret and Nathan spent a total of $128 at the state fair last weekend. Nathan spent $2 more than twice the amount that Margaret spent. How much did Nathan spend at the fair?
Let 'y' represent the amount Margaret spent at the state fair.
Let 'x' represent the amount Nathan spent at the state fair.
In the next statement, Nathan spent $2 more than twice the amount that Margaret spent.
Mathematically,
[tex]x=2+2y\ldots\ldots.1[/tex]And also, we were told that Margaret and Nathan spent a total of $128 at the state fair.
Mathematically,
[tex]x+y=\text{ \$128}\ldots\ldots\ldots2[/tex]Let us substitute 'x'= 2+2y into equation 2 and solve for y.
[tex]\begin{gathered} x+y=128 \\ 2+2y+y=128 \\ 2y+y=128-2 \\ 3y=126 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3y}{3}=\frac{126}{3} \\ y=42 \end{gathered}[/tex]Therefore, the amount of money spent by Nathan will be,
[tex]\begin{gathered} x=2+2y \\ x=2+2(42)=2+84=86 \\ \therefore x=86 \end{gathered}[/tex]Hence, Nathan spent $86 at the fair.
24. Which point is part of the solution for the system of inequalities graphed below? A. (-1,-2) B. (3,1) C. (1,-2) D. (-3,1)
The solution must be insige the red grind so we can see that the only point inside this area is the coordinate (-3, 1) so the answer is D
how do i find the volume to the nearest 1 decimal place?
Solution:
The volume of a cylinder is expressed as
[tex]\begin{gathered} V=\pi\times r^2\times h \\ where \\ V\Rightarrow volume\text{ of the cylinder} \\ r\Rightarrow radius\text{ of its circular ends} \\ h\Rightarrow height\text{ of the cylinder} \end{gathered}[/tex]Given the cylinder below:
we have
[tex]\begin{gathered} height\text{ of the cylinder = 4 cm} \\ diameter\text{ of the circular end = 2 cm} \end{gathered}[/tex]but
[tex]\begin{gathered} radius=\frac{diameter}{2} \\ \Rightarrow r=\frac{d}{2}=\frac{2cm}{2}=1\text{ cm} \end{gathered}[/tex]Thus, the volume of the cylinder is evaluated by substituting the values of 4 cm and 1 cm for h and r respectively into the volume formula.
[tex]\begin{gathered} V=\pi\times1cm\times1cm\times4cm \\ =12.56637 \\ \approx12.6\text{ cubic centimeters} \end{gathered}[/tex]Hence, the volume of the cylinder, to the nearest 1 decimal place is
[tex]12.6\text{ cubic centimeters}[/tex]You roll a six-sided dice.Event A: Roll a 6. Event B: Roll a prime number. Find P(A or B) . Express your answer as a fraction in simplest form.
The probability of rolling a 6 is:
[tex]P(A)=\frac{1}{6}[/tex]There are 3 prime numbers between 1 and 6: 2, 3 and 5. Therefore, the probability of rolling a prime number is:
[tex]P(B)=\frac{1}{3}[/tex]Therefore, the probability of rolling a 6 or a prime number is:
[tex]P(AorB)=\frac{1}{6}+\frac{1}{3}=\frac{1}{2}[/tex]Solve the equation. (Enter your answers as a comma-separated list.)2b2 − 18 = −9b
Given
The equation,
[tex]2b^2-18=-9b[/tex]To solve for b.
Explanation:
It is given that,
[tex]2b^2-18=-9b[/tex]That implies,
[tex]\begin{gathered} 2b^2-18=-9b \\ 2b^2+9b-18=0 \\ 2b^2-3b+12b-18=0 \\ b(2b-3)+6(2b-3)=0 \\ (2b-3)(b+6)=0 \\ 2b-3=0,b+6=0 \\ 2b=3,b=-6 \\ b=\frac{3}{2},b=-6 \end{gathered}[/tex]Hence, the answer is 3/2, -6.
Statement Reason
1. AEEC;BDDC 1. given
2. ∠AEC is a rt. ∠; ∠BDC is a rt. ∠ 2. definition of perpendicular
3. ∠AEC ≅ ∠BDC 3. all right angles are congruent
4. ? 4. reflexive property
5. △AEC ~ △BDC 5. AA similarity theorem
What is the missing statement in step 4?
The missing Statement is 4. ∠EAC ≅ ∠EAC 4. reflexive property
In △AEC and △BDC
We need to know the missing statement in step 4
Statement Reason
1. AE⊥EC;BD⊥DC 1. given
2. ∠AEC is a rt. ∠; ∠BDC is a rt. ∠ 2. definition of perpendicular
3. ∠AEC ≅ ∠BDC 3. all right angles are congruent
4. ∠EAC ≅ ∠EAC 4. reflexive property
5. △AEC ~ △BDC 5. AA similarity theorem
Therefore, the missing Statement is 4. ∠EAC ≅ ∠EAC 4. reflexive property.
To learn more about similarity properties refer here
https://brainly.com/question/24184322
#SPJ1
help pls 1st blank - Graph A, Graph B, Graph C, Graph D 2nd blank - Yes or No 3rd blank - inside or outside
SOLUTION
From the question,
Let x represent acres for apple orchard
Let y represent acres for peach orchard
Since the farmer can afford a maximum of 54 acres of land, that means
[tex]x+y\le54[/tex]The apple orchard requires 3000 gallons of water, while the peach requires 800 gallons of water. But the farmers irrigation system can deliver a maximum of 80,000 gallons per day, puting in an equation, we have
[tex]3000x+800y\le80,000[/tex]From his apple orchard, he expects to get a profit of $3,400 per year and from peach, a profit of $1,600 per year.
His expected profit will be determined using the equation
[tex]\begin{gathered} P=3400x+1600y \\ \text{where P is the expected maximum profit } \end{gathered}[/tex]So, we will plot the following points
[tex]\begin{gathered} x+y\le54 \\ 3000x+800y\le80,000 \end{gathered}[/tex]This will help us to get the required region needed to find the expected maximum profit
We can see that this is the same with graph B from the question
Now, we will substitute the following points from the graph into the equation of the maximum expected profit. Which ever that gives us the highest value becomes the answer.
For point (0, 54) we have
[tex]\begin{gathered} P=3400x+1600y \\ P=3400(0)+1600(54) \\ P=0+86,400 \\ P=86,400 \end{gathered}[/tex]For Point (16.727, 37.273), we have
[tex]\begin{gathered} P=3400x+1600y \\ P=3400(16.727)+1600(37.273) \\ P=56,871.8+59,636.8 \\ P=116,508.6 \end{gathered}[/tex]Finally, for point (26.667, 0) we have
[tex]\begin{gathered} P=3400x+1600y \\ P=3400(26.667)+1600(0) \\ P=90,667.8+0 \\ P=90,667.8 \end{gathered}[/tex]We can see that the maximum profit is $116,508.60, from
point (16.727, 37.273)
Hence the division of land that will maximize his expected profit is
16.73 acres of land for apple orchard
37.27 acres of land for peach orchard
Now, looking at the graph, the point (30, 20) lies outside the required region, so the farmer cannot maximize his profit at 30 acres for apple orchard and 20 acres for peach orchard.
Hence the answer is No, because the point (30, 20) lies outside the solution region.
which point on the grid below has coordinates (-9, -2)?
Answer:
A
Explanation:
Given the point (-9,-2):
[tex]\begin{gathered} (x,y)=(-9,-2) \\ \implies x=-9,y=-2 \end{gathered}[/tex]As seen in the graph, the point on the grid that has the coordinates (-9,-2) is point A.
What percentage of the data values falls between the values pf 3 and 24 in the data set shown? 0 5 10 15 20 25 O 25% O 50% O 75% O 100%
The graph shown in the image is a box and whiskers plot.
The sides of the box are determined by the first and third quartiles of the sample.
The left side corresponds to the first quartile (Q₁), this value separates the bottom 25% of the sample from the top 75%
The right side corresponds to the third quartile (Q₃), this value separates the bottom 75% of the sample from the top 25%
The line inside the box represents the second quartile (Q₂), this value is also known as the Median of the sample and divides the bottom 50% from the top 50%.
The body of the box, i.e. the space between Q₁ and Q₃, is the interquartile range (IQR), this represents the mid 50% of the sample.
The left whisker links the first quartile with the minimum value of the sample.
The right whisker links the third quartile with the maximum
Assume that when adults with smartphones are randomly selected, 49% use them in meetings or classes. If 11 adult smartphone users are randomly selected, findthe probability that fewer than 4 of them use their smartphones in meetings or classes.The probability is
Answer: 12.66%
First, we will solve the probability that 3 adults, 2 adults, 1 adult and no adult use their smartphones in meetings or classes,
To solve for this, we will use the following equation
[tex]11Cn\times0.49^n\times0.51^{11-n}[/tex]*Probability of adults using their phones for meetings or classes are 0.49.
1 - 0.49 = 0.51
*Probability of adults NOT using their phones are 0.51
Now, with the values of n at:
n = 0
n = 1
n = 2
n = 3
[tex]11Cn\times0.49^n\times0.51^{11-n}=11C0\times0.49^0\times0.51^{11-0}=0.0006[/tex][tex]11Cn\times0.49^n\times0.51^{11-n}=11C1\times0.49^1\times0.51^{11-1}=0.0064[/tex][tex]11Cn\times0.49^n\times0.51^{11-n}=11C2\times0.49^2\times0.51^{11-2}=0.0308[/tex][tex]11Cn\times0.49^n\times0.51^{11-n}=11C3\times0.49^3\times0.51^{11-3}=0.0888[/tex]Now, we will add these altogether to get the probability that fewer than 4 of them use their smartphones in meetings or classes.
[tex]0.0006+0.0064+0.0308+0.0888=0.1266=12.66\%[/tex]The answer would be 12.66%.
Which conjecture is possible to prove?A. All quadrilaterals with at least one side length of 3 are congruent.B. All rectangles with at least one side length of 3 are congruent.C. All rhombuses with at least one side length of 3 are congruent.D. All squares with at least one side length of 3 are congruent.
All the sides of a square are equal, therefore, if at least one side length is congruent, all of them are.
Thus,
The correct answer is option D.
my name is Emma I'm 9 years old I'm in third grade
From the question we can deduce that, the squares shaded in red represent the area tomatoes are planted in the garden.
The squares unshaded represents the area corn is planted in the garden.
Observe carefully that the total squares shaded in red are 24 (that is 4 by 6 OR 4 times 6). The unshaded squares total 18 (that is 3 times 6).
Each unit (or each square) is 1 square foot. This means on Nora's garden, she has tomatoes planted on 24 square feet. Also she has corn planted on 18 square feet.
Therefore, the difference between both areas is
Difference = 24 - 18
Difference = 6
ANSWER:
There are 6 more square feet of tomatoes than corn in Nora's garden.
The correct answer is option D
(5x^5-y)^2 binomials to power
Answer:
The expansion of the expression gives;
[tex]=25x^{10}-10x^5y+y^2[/tex]Expansion:
Given the expression:
[tex](5x^5-y)^2[/tex]We want to expand;
[tex]\begin{gathered} (5x^5-y)^2 \\ =(5x^5-y)(5x^5-y) \\ =5x^5(5x^5-y)-y(5x^5-y) \\ =5x^5(5x^5)+5x^5(-y)-y(5x^5)-y(-y) \\ =25x^{10}-5x^5y-5x^5y+y^2 \\ =25x^{10}-10x^5y+y^2 \end{gathered}[/tex]Therefore, the expansion of the expression gives;
[tex]=25x^{10}-10x^5y+y^2[/tex]3) Graph y=-3 (x - 2)2 + 3
The equation is:
[tex]y=-3(x-2)^2+3[/tex]So this is a parabola, so we can graph it with the vertex and the intercections with the x axis
So the vertex is in the coordinat (2,3) becuase of the transformation of -2 in the x axis and +3 in the y axis so the vertex is (2, 3)
now for the interception with the x axis we replace y = 0 and solve for x so
[tex]0=-3(x-2)^2+3[/tex]we open the parenthesis like:
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