The given sequence is
[tex]-7,-3,1,5[/tex]To find the explicit formula, first, we have to find the difference by subtracting two consecutive terms.
[tex]-3-(-7)=-3+7=4[/tex]As you can observe, the difference is 4.
[tex]d=4[/tex]From the sequence, we observe that the first term is -7.
[tex]a_1=-7[/tex]The formula for arithmetic sequences is
[tex]a_n=a_1+(n-1)d[/tex]Now, let's replace the values we've got.
[tex]a_n=-7+(n-1)\cdot4[/tex]Then, we simplify.
[tex]\begin{gathered} a_n=-7+4n-4 \\ a_n=4n-11 \end{gathered}[/tex]Therefore, the right answer is D.Mrs. Smith spent $50 more at a store than mrs. Jones. Combined they spent at most $250. What is the most they each could have spent?
By working with inequalities, we will see that:
Mrs. Jones can spend between $0 and $100.Mrs. Smith can spend between $50 and $150.How much each spent?Let's define:
S = amount that Mrs. Smith spent.J = amount that Mrs. Jones spentWe know that Mrs. Smith spent $50 more at a store than Mrs. Jones, then:
S = J + 50
And together they spent at most $250, then:
S + J ≤ 250
Now, replacing the equation in the inequality, we get:
(J + 50) + J ≤ 250
2*J + 50 ≤ 250
2*J ≤ 250 - 50
2*J ≤ 200
J ≤ 200/2
J ≤ 100
So Mrs. Jones spent at most 100 dollars.
And Mrs Smith spent $50 more than that, so we can write the inequality.
50 ≤ S ≤ 150
She spends between $50 and $150.
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The slant height and the base of the cone are in the ratio 2:1. If the radius of the cone is 145cm. What is the total surface area of the cone?
The most appropriate choice for cone and total surface area of cone will be given by-
Total surface area of the cone is [tex]198235.71 cm^2[/tex]
What is cone and total surface area of cone?
Cone is a 3 dimensional figure whose base is a circle and upper surface finally converge to a point.
Cone is obtained by revolving a right angled triangle about one of its legs.
Total surface area of the cone is the sum of curved surface area of the cone and the area of the base of the cone.
If r is the radius of the base of the cone and l is the slant height of the cone, then total surface area of the cone will be given by
[tex]\pi r(r+l)[/tex]
Here
Ratio of the slant height and radius of base of the cone = 2:1
Radius = 145cm
Slant height = [tex]145 \times 2[/tex]
= 290 cm
Total surface area of cone = [tex]\pi r(r+l)\\[/tex]
= [tex]\frac{22}{7} \times 145\times (145+290)\\[/tex]
= [tex]\frac{22}{7} \times 145 \times 435[/tex]
= [tex]198235.71 cm^2[/tex]
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Complete Question
The slant height and the radius of base of the cone are in the ratio 2:1. If the radius of the cone is 145cm. What is the total surface area of the cone?
The tape diagram represents the ratio of your monthly allowance to your friend's monthly allowance. The monthly allowances total $72.How much is each allowance?
you [][][][][]
friend[][][][]
The allowance of each person is
You: $40Friend: $32How to determine the amount of each person's allowance?From the question, the tape diagram that can be used in our computation is given as
you [][][][][]
friend[][][][]
Counting the number of boxes, we have
You = 5
Friend = 4
Next, we represent the boxes as a ratio
So, we have
You : Friend = 5 : 4
This means that
You = 5/9 * Total allowance
Friend = 4/9 * Total allowance
From the question, we have
Total allowance = $72
Substitute the known values in the above equation
So, we have the following equation
You = 5/9 * 72
Friend = 4/9 * 72
Evaluate the products
You = 40
Friend = 32
Hence, the amount of each person's allowance is $40 and $32, respectively
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a student measures which method of taking notes improves grades more, using a computer or a pencil and paper. what type of study is described?Sample StudyExperiment Observational Study Cluster Study
Since the student is meausuring something we conclude that this is an experiment.
The entire graph of the function g is shown in the figure below.
Write the domain and range of g using interval notation.
(a) domain=
(b) range =
HELP ASAP Determine the values of x in the equation x2 = 81.
x = −9
x = ±9
x = ±40.5
x = 40.5
The value of x in the given quadratic equation are; +9 and -9.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. An equation of degree 2 containing a single variable is known as the quadratic equation. Its general form is ax² + bx + c = 0 , where variables are x and constants are a, b, and c.
As equation is x²= 81
Taking square root on both sides;
⇒ √x² = √81
⇒ X = ± 9
Thus the value of X is ± 9
Hence, The roots of the given quadratic equation are; +9 and -9.
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Under his cell phone plan, Deion pays a flat cost of $39 per month and $4 per gigabyte. He wants to keep his bill at $49.40 per month. How many gigabytes of data can he use while staying within his budget?
Answer:
(49.4 - 39) / 4
= 10.4 / 4
= 2.6GB
Step-by-step explanation:
From the diagram below, what is the measure of the angle of depression from point A
The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.
From point A, point B is observed with an angle of 45 down from the top of the tree to the ground.
Thus, the angle of depression is 45°
A cyclist rides her bike at a rate of 8 miles per hour. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 2 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers. Rate:km/hDistance traveled in 2 hours:km
Given:
1 mile = 1.6 km
So, 8 miles per hour in kilometers per hour is given by:
[tex]\frac{1}{8}=\frac{1.6}{x}[/tex]Where x = # of kilometers
So, solve for x:
[tex]\begin{gathered} x\cdot1=1.6\cdot8 \\ x=12.8 \end{gathered}[/tex]This is 12.8 km per hour
Next, the distance traveled in 2 hours is:
[tex]rate=\frac{distance}{time}\rightarrow distance=rate\times time[/tex]Substitute the values:
[tex]distance=12.8\times2=25.6[/tex]Answer:
Rate: 12.8 km/h
Distance traveled in 2 hours: 25.6 km
What percent of 90 is 200?
Luna brought all her savings with her to Rome, in euros. For the first week, she spent the same amount of money each day. The table shows how much Luna had left at the end of each day. What was the initial value of Luna's savings? Day Euros ? 315 1 2 280 3 245 4 210 5 175 6 140 7 105 35 euros 315 euros 80 euros 350 euros
every day she spent $35, if after 1 day she still have $315, the day before that she had $315+$35=$350
Therefore, the initial value was $350
Solve each system of equations please show your work! 3x+y-2z=22 x+5y+z=4 x=-3z
The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The system of the equations are,
3x + y - 2z = 22 .... (i)
x + 5y + z = 4 .... (ii)
x = - 3z .... (iii)
Now,
Solve the equations as;
Substitute x = - 3z in both equations, we get;
⇒ 3x + y - 2z = 22
⇒ 3 × -3z + y - 2z = 22
⇒ - 9z + y - 2z = 22
⇒ - 11z + y = 22 .... (iii)
And, x + 5y + z = 4
- 3z + 5y + z = 4
5y - 2z = 4 ... (iv)
Solve equation (iii) and (iv) we get;
⇒ y = 44 and z = 2
So, x = - 3z
⇒ x = - 3 × 2
⇒ x = - 6
Thus, The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
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Determine the continuity at x = 2. Be sure to clearly state your reasoning. fastest answer get ranked brainliest
The answer is in my screenshot pic.
(2 3/5) Multiply (-2 2/3)
[tex] \frac{13}{5} \times - \frac{8}{3} \\ = - \frac{104}{15} [/tex]
ATTACHED IS THE SOLUTION
Answer:
(-104/15)
Step-by-step explanation:
3 2
2 ------ × -2 -------
5 3
5 × 2 = 10
10 + 3 = 13
3 × -2 = -6
-6 + -2 = -8
13 -8 104
------- × ------- = (-) -------
5 3 15
I hope this helps!
Achromycin is to be administered 11mg per pound in 4 equal doses to a patient weighing 34kg. Oral suspension is available 125mg per 5mL. How many millilitres should you give per dose? Use 1 kg = 2.2 lbs and round your final answer to 1 decimal place.
We are told that 11 mg of Achromycin per patient pound must be administered, we are also given the weight of the patient as 34 kg, in order to properly use this weight we must convert it from kg to pounds by multiplying the weight in kg by 2.2, like this:
34×2.2 = 74.8
Then, the patient weight is 74.8 lbs, by multiplying this by the 11 mg per pound of Achromycin that have to be administered we can determine the mg of Achromycin, like this:
74.8×11 = 822.8
Then, 822.8 mg of Achromycin has to be administered, by dividing this amount by 4, we can determine the amount for each dose:
822.8/4 = 205.7
Then 205.7 mg are given per dose, since 5 mL contains 125 mg, we can take the ratio of mL to mg to get:
5/125 = 1/25
By multiplying the above ratio by 205.7 we can determine the milliliters that should be given per dose, like this:
205.7×1/25 = 8.2
Then, 8.2 mL must be given per dose
Real world compositionsShoe sizes are marked differently in many countries. In Japan, a shoe size is 16 more than the size in the United States. In Korea, a shoe size is 224 more than the size in Japan. Determine the function of the U.S. size of a shoe in terms of the shoe size in Korea. What is the U.S. shoe size of a shoe that is 250 in Korea? Solve using composite functions
To solve this exercise, we define the following variables:
• j = Japan size of shoes,
,• u = United Sates size of shoes,
,• k = Korea size of shoes.
From the statement of the problem, we know that:
0. In Japan, shoe size is 16 more than the size in the United States →, j = 16 + u,,
,1. In Korea, shoe size is 224 more than the size in Japan →, k = 224 + j.
We must find a function for the U.S. size of a shoe (u) in terms of the shoe size in Korea (k).
1) From point 1, we have:
[tex]\begin{gathered} j=16+u, \\ u=j-16. \end{gathered}[/tex]2) From point 2, we have:
[tex]\begin{gathered} k=224+j, \\ j=k-224. \end{gathered}[/tex]Replacing the expression of j in terms of k in the expression of u, we get:
[tex]u=j-16=(k-224)-16=k-240.[/tex]Replacing the value k = 250 in the last equation, we get:
[tex]u=250-240=10.[/tex]Answer
The U.S. shoe size of a shoe that is 250 in Korea is equal to 10.
determine the answer to the nearest tenth of a percent.12 out of 52 cards in a deck are face cards.What percentage of cards in a deck are face cards?
Total number of cards: 52
Number of face cards: 12
To calculate the percentage that the face cards represent we need to divide the number of face cards by the total number of cars, and then multiply by 100%:
[tex]\frac{12}{52}\times100[/tex]The first division 12/52 will give us the proportion that the face cards represent, and by multiplying that by 100 we find the percentage.
Solving the operations:
-solving the division
[tex]0.2308\times100[/tex]-solving the multiplication:
[tex]23.08[/tex]The face cards represent 23.08%.
Rounding to the nearest tenth of a percent (one decimal place):
[tex]\approx23.1[/tex]Answer: 23.1%
Use the inverse trigonometric keyson a calculator to find the measureof angle A
ANSWER
A = 51°
EXPLANATION
ABC is a right triangle. We know the length of the hypotenuse, AB = 44 m, and the length of the adjacent leg to angle A, AC = 28 m. To find the measure of angle A we have to use the cosine of that angle,
[tex]\cos A=\frac{AC}{AB}[/tex]Solving for A,
[tex]A=\cos^{-1}\left(\frac{AC}{AB}\right)[/tex]Replace with the known values and solve,
[tex]A=\cos^{-1}\left(\frac{28}{44}\right)=\cos^{-1}\left(\frac{7}{11}\right)\approx50.4788\degree\approx51\degree[/tex]Hence, the measure of angle A is 51°, rounded to the nearest whole number.
A person invests $6,750 in an account that earns 5.25% annual interest compounded continuously. Findwhen the value of the investment reaches $15,000. If necessary round to the nearest tenth.The investment will be reach $15,000 in approximatelyyears.
Recall the formula for the Future value of a principal amount, compounded continuously.
[tex]\begin{gathered} A=Pe^{rt} \\ \text{where} \\ A\text{ is the Future Value} \\ P\text{ is the Principal amount} \\ r\text{ is the rate in decimals} \\ t\text{ is time in years} \end{gathered}[/tex]Rearrange the equation so that we can solve for time t.
[tex]\begin{gathered} A=Pe^{rt}^{} \\ \frac{A}{P}=\frac{Pe^{rt}}{P} \\ \frac{A}{P}=e^{rt} \\ e^{rt}=\frac{A}{P} \\ \ln e^{rt}=\ln \mleft(\frac{A}{P}\mright) \\ rt\ln e^{}=\ln \mleft(\frac{A}{P}\mright) \\ rt^{}=\ln \mleft(\frac{A}{P}\mright) \\ \frac{rt}{r}=\frac{\ln (\frac{A}{P})}{r} \\ t=\frac{\ln(\frac{A}{P})}{r} \end{gathered}[/tex]Now substitute the following given and we have
[tex]\begin{gathered} t=\frac{\ln(\frac{A}{P})}{r} \\ t=\frac{\ln (\frac{15000}{6750})}{0.0525} \\ t=\frac{\ln (\frac{20}{9})}{0.0525} \\ t=15.2096704\text{ years} \end{gathered}[/tex]Rounding the answer to the nearest tenth, the investment will reach $15000, in approximately 15.2 years.
a crew can clear 1/2 ton of dirt in 30 minutes. how many tons can they clear in 4 hours
Answer: 4 tons
Step-by-step explanation:
Since the crew can clear 1/2 ton in 30 minutes, 4 hours has eight 30 minutes, which means that 8x1/2 = 4
Answer: 4 tons
Step-by-step explanation:
30 minutes multiplied by 2 is 1 hour and 1 half times 2 is 1 ton, so the crew can clear one ton every hour. 4 hours times 1 ton is 4 tons an hour.
what is the lcm of the rational algebraic equation 6/x+x-3/4=2
The required answer would be (24 -3x - 4x²) / 4x = 0 which is the lcm of the rational algebraic equation 6/x+x-3/4=2.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The given equation below as:
⇒ 6/x + x - 3/4 = 2
We have to determine the lcm of the rational algebraic equation
⇒ 6/x + x - 3/4 = 2
Rearrange the term of 2 in the equation,
⇒ 6/x + x - 3/4 - 2 = 0
Take LCM in the above equation,
⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]
⇒ (24 + 4x² -3x - 8x²) / 4x = 0
Combine the likewise terms in the numerator,
⇒ (24 -3x - 4x²) / 4x = 0
Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.
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I need this answered From my prep guid, pre calc
Given:
The equation of the ellipse is,
[tex]\frac{(x-2)^2}{36}+\frac{(y+3)^2}{12}=1[/tex]Explanation:
The general equation of ellipse with center (h,k) is,
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]The center of te given ellipse is (2,-3).
Determine the value of a and b.
[tex]\begin{gathered} a=\sqrt[]{36} \\ =6 \end{gathered}[/tex][tex]\begin{gathered} b=\sqrt[]{12} \\ =2\sqrt[]{3} \end{gathered}[/tex]The value of a is more than b. so major axis is horiontal and minor axis is vertical.
The coordinates of endpoints of major axis are,
[tex](2+6,3)=(8,-3)[/tex]and
[tex](2-6,3)=(-4,-3)[/tex]The coordinates of endpoints of minor axis,
[tex](2,-3+2\sqrt[]{3})[/tex]and
[tex](2,-3-2\sqrt[]{3})[/tex]or we can expressed coordinates of endpoints of minor axis as,
[tex](2,-3\pm2\sqrt[]{3})[/tex]please helpppppppppppppp
Answer:
Step-by-step explanation:
Substitute a and b with 1/4 and 6
5b/ 32a^2
5(6)/ 32(1/4)^2
30/32(1.96)
30/62.72
0.5102 Answer
Fill in the blank to correctly complete the sentence.
Consider the following function.
f(x)
=
2x4+6x3−4x2+2x+12
=
x−2)2x3+10x2+16x+34+80
By inspection, we can state that f(2)=
The value of f(2) would be 80 which is determined by substituting the value of x = 2in the given function f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80.
What is a function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The given function below is:
f(x) = 2x⁴ + 6x³ −4x² +2x + 12
f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80
We have to determine the value of f(2).
⇒ f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80
Substitute the value of x = 2 in the given function,
⇒ f(x) = (2 −2)(2(2)³ + 10(2)² + 16(2) + 34) + 80
⇒ f(x) = (0)(2(2)³ + 10(2)² + 16(2) + 34) + 80
⇒ f(x) = 0 + 80
⇒ f(x) = 80
Therefore, the value of f(2) would be 80.
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How do scatter plots and histograms differ from line graphs?
None of the above
All three are used synonymously
Scatter plots and histograms show trends, or how data changes over time while line
graphs show how data is distributed.
Scatter plots and histograms show how data is distributed while line graphs show
trends, or how data changes over time.
Answer: Scatter plots, to show relationships among numerical variables. Line graphs, to show change over time. Histograms, to show data distributions.
Step-by-step explanation: I looked it up
The sales tax in Arizona is 7.5%. The price tag on a T-shirt in Arizona says $11.50. What is the sales tax, in dollars, for this item?
Answer:
$0.8625
Explanation:
The sales tax for the t-shirt will be 7.5% of the price. So, 7.5% of $11.50 can be calculated as:
[tex]\text{ \$11.50 }\times\text{ 7.5\% = 11.50}\times\frac{7.5}{100}=\text{ \$0.8625}[/tex]So, the sales tax for this item is $0.8625
It takes 4 oranges to makes 6 ounces of orange juice. What are the two unit rates?
Answer: The second ratio in the proportion is set up as ounces over oranges. The units should be in the same place in proportion to the first ratio.
Step-by-step explanation:
PLS HELP ME WITH THIS QUESTION ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The value of (x) will be equal to → x = 16 - K.
What is the perimeter?
Perimeter is the measure of the length of the boundary of any two dimensional shape.
Given is a quadrilateral with its sides given.
The perimeter of this quadrilateral will be the sum of the length of its sides. Since, in the question, the final value of perimeter is not given, therefore we will assume it as K. The perimeter will be equal to -
(7x - 1) + (- 8x - 5x) + (6x + 13) + (4 - x) = K
7x - 1 - 8x - 5x + 6x + 13 + 4 - x = K
16 - x = K
x = 16 - K
Therefore, the value of (x) will be equal to → x = 16 - K.
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Can someone pls help me find the equation for the arithmetic sequence and help me fill out the graph
Solution
- The question gives us the following arithmetic sequence:
[tex]t(n+1)=t(n)-4[/tex]- We are asked to write out the explicit function for the sequence.
- To do this, we simply write out the terms of the sequence. After this, we would determine the common difference of the sequence.
- We will use the common difference to find the first term of the sequence and then use the formula below to find the explicit form of the arithmetic sequence:
[tex]\begin{gathered} t(m)=a+(m-1)d \\ \text{where,} \\ a=\text{first term of the sequence} \\ d=\text{common difference} \\ m=\text{ number of terms} \\ \\ (\text{Note that: }m=n+1\text{, since the formula starts assumes that the sequence starts from the 1st term not zeroth term} \end{gathered}[/tex]- We have been given that the second term of the sequence is 10. We would also use this term to form our sequence.
[tex]\begin{gathered} \text{Let n=2} \\ \text{The formula becomes} \\ t(2+1)=t(2)-4 \\ t(3)=t(2)-4 \\ \\ \text{But we know that }t(2)=10 \\ \therefore t(3)=10-4 \\ t(3)=6 \\ \\ \text{Let n=3} \\ t(3+1)=t(3)-4 \\ t(4)=6-4 \\ t(4)=2 \\ \\ \text{Let n=4} \\ t(4+1)=t(4)-4 \\ t(5)=2-4 \\ t(5)=-2 \\ \\ \text{Thus, we can write out the terms of the sequence as follows:} \\ \ldots,t(2),t(3),t(4),t(5),\ldots=\ldots10,6,2,-2\ldots \\ \\ \text{ We can observe that the common difference is -4 since,} \\ 6-10=-4 \\ 2-6=-4 \\ -2-2=-4 \\ \text{And so on}\ldots \\ \\ \text{Thus, we can trace our sequence back to its first term as follows:} \\ t(2)-t(1)=-4 \\ 10-t(1)=-4 \\ \text{Subtract 10 from both sides} \\ -t(1)=-4-10 \\ \therefore t(1)=14 \\ \\ t(1)-t(0)=-4 \\ 14-t(0)=-4 \\ \text{Subtract 14 from both sides} \\ -t(0)=-4-14=-18 \\ \therefore t(0)=18. \\ \\ \text{Thus, the first term }t(0)=18 \end{gathered}[/tex]- Let us now apply the formula for the nth term of a sequence to find the explicit formula:
[tex]\begin{gathered} first\text{ term =}t(0)=a=18 \\ \text{common difference}=d=-4 \\ t(m)=a+(m-1)d \\ \\ t(m)=18+(m-1)(-4) \\ \text{Expand the bracket} \\ t(m)=18+m(-4)-1(-4) \\ t(m)=18-4m+4 \\ \\ \therefore t(m)=22-4m \\ \\ \text{Let us write the sequence in terms of n} \\ m=n+1 \\ t(n)=22-4(n+1) \\ t(n)=22-4n-4 \\ t(n)=18-4n \\ \\ \text{Thus, the explicit function is:} \\ t(n)=18-4n \end{gathered}[/tex]- With the above formula, we can proceed to populate the table. Let us use the formula to calculate all the terms for each value of n.
[tex]\begin{gathered} t(n)=18-4n \\ \\ \text{when n = 0} \\ t(0)=18-4(0) \\ t(0)=18 \\ \\ \text{when n= 1} \\ t(1)=18-4(1) \\ t(1)=14 \\ \\ \text{when n=2} \\ t(2)=18-4(2) \\ t(2)=10 \\ \\ \text{when n = 3} \\ t(3)=18-4(3) \\ t(3)=18-12=6 \\ \\ \text{when n = 4} \\ t(4)=18-4(4) \\ t(4)=2 \\ \\ \text{when n = 5} \\ t(5)=18-4(5) \\ t(5)=-2 \end{gathered}[/tex]- On the table, we have the values filled in below:
Final Answer
The explicit form of the sequence is:
[tex]t(n)=18-4n[/tex]Look Ahead To find the new temperature, you found the sum of a positive anda negative integer. You can use a number line to help you think about addinga. During the day, the temperature at another weather station is 4°C. Overnight,it changes by-9°C Enrico models the situation on the number line below.Hasina says she can model it with one arrow. How can she model the situationLook Back whalHow do you know?positive and negative numbers.with just one arrow?434520 1-3 -2 -1
Let's begin by listing out the information given to us: