⇒[tex]T_{n} =a+(n-1)d[/tex] is the formula to find the general term of the arithmetic sequence.
⇒Note to find the second term we will plug in 2 in the place of n in the formular and simplify.
⇒[tex]T_{2} =a+(2-1)d\\T_{2} =a+(1)d\\T_{2} =a+d[/tex]
⇒It is given that the second term is 7 meaning in the place of [tex]T_{2}[/tex] in the equation above since we do not know the value of a and d we will plug in 7 and have the equation [tex]7=a+d[/tex] as our first equation.
⇒ For the fourth term [tex]T_{4}[/tex] we follow the same step of using the general formula to find the nth term by plugging in 4 in the place of n and and simplify
[tex]T_{4} =a+(4-1)d\\T_{4}=a+(3)d\\T_{4}=a+3d[/tex]
In the place of [tex]T_{4}[/tex] plug in 1 for the fourth term is equal to 1 to have the second equation
[tex]1=a+3d[/tex]
Note we can now use the two equations we have now to find the value of a which is the first term and d which is the difference.
7=a+d......1st equation
1=a+3d...2nd equation
∴from the first equation by making a the subject of the equation we get
a=7-d
from the second equation making a the subject of the equation we get a=1-3d
Now let us equate first equation and the second equation since they are both equal to a and solve for d.
[tex]7-d=1-3d\\-d+3d=1-7\\2d=-6\\\frac{2d}{2} =\frac{-6}{2} \\d=-3[/tex]
⇒Now you can see that we have the difference of the arithmetic sequence equal to -3
⇒To find the value of a you can use any of the equations from the ones we created . I will use the equation a=7-d
[tex]d=-3\\a=7-d\\a=7-(-3)\\a=7+3\\a=10[/tex]
⇒ to get the 15th term we will go back to the general formula of finding the nth term in the place if n we will plug in 15 and simplify the formula
[tex]T_{15} =a+(15-1)d\\T_{15}=a+(14)d\\T_{15}=a+14d\\[/tex]
⇒Now we find that the 15th term is equal to a plus 14(d)
⇒Note we already have the value of a and we can just plug them in to find the value of the 15th term and simplify.
[tex]a=10,d=-3\\T_{15}=a+14d\\\\T_{15}=10+14(-3)\\T_{15}=10-42\\T_{15}=-32[/tex]
⇒The 15th term is -32
When 12 is added to half the sum of a number and 8, the result is 40. What is the number?
When 12 is added to half the sum of a number and 8, the result is 40, the number is 48.
Let the number be x.
According to question,
12 + (x + 8)/2 = 40
(x + 8)/2 = 40-12
(x + 8)/2 = 28
x + 8 = 28*2
x + 8 = 56
x = 56 - 8
x = 48
Hence, the number is 48.
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Write the percent as a decimal. Round to the nearest thousandth if the division does not terminate.5/40%=
ANSWER
[tex]0.001[/tex]Given;
[tex]\frac{5}{40}\%[/tex]Firstly, convert to decimal
we have;
[tex]\begin{gathered} \frac{5}{40}\% \\ =0.125\% \\ \end{gathered}[/tex]"Percent" means "per 100" or divide by 100
Hence, we have;
[tex]\begin{gathered} \frac{0.125}{100} \\ =0.00125 \\ \end{gathered}[/tex]now, converting to the nearest thousandth
[tex]\begin{gathered} =0.00125 \\ \equiv0.001 \end{gathered}[/tex][tex]\equiv0.001[/tex]The answer to the nearest thousandth is
[tex]0.001[/tex]Camila invested $4,400 in an account that is earning an interest rate 90% every year. Camilla wants to create an exponential equation that allows her to track the interest earned over time, M(t).
Given:
Principal Amount, P = $4,400
Interest rate, r = 90%
Here, Camilla needs to create an exponential equation that allows her tract the interest earned over time.
This is a Compound interest problem.
To find create an exponential equation, apply the formula below:
[tex]I=P(1+r)^t-P[/tex]WHere:
P is the principal amount = $4,400
r is the rate = 90% = 0.90
t is the time (number of years)
Input values into the equation above:
[tex]M(t)=4400(1+0.9)^t-4400[/tex]Therefore, the exponential equation that allows her to track the interest earned over time is:
[tex]M(t)=4400(1+0.9)^t-4400[/tex]Plugging the value for the number of years for t, you will get the interest earned over time, t.
ANSWRER:
[tex]M(t)=4400(1+0.9)^t-4400[/tex]Lines AB and CD (if shown) are straight lines. Find x .
By using properties of angles, it is obtained that
x = 20°,
What is an Angle?
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Here,
[tex]m\angle DOB =m\angle DOE +m\angle EOB[/tex] [ Addition of two angles]
[tex]m\angle DOB =90+x[/tex] [ Substitution]
[tex]m\angle AOC = m\angle DOB[/tex] [Vertically opposite angle]
[tex]110 = 90 + x[/tex] [ Substitution]
[tex]x = 20^{\circ}[/tex] [Algebra]
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Given the information in the image below, find the measure of angle N. Explain how you arrived at this answer. Be sure to use key terms such at “isosceles triangle,” vertical angles,” and “congruent,” etc. You should at least have four sentences.
In the triangle LMN angle N is 76 degree.
Given,
In the question:
There is two isosceles triangle in the figure:
Triangle JKL and Triangle LMN
Angle J = 64 degree
To find the angle Angle N
Now, According to the question:
The triangle is isosceles.
<J = 64 degrees
All triangles have 180
<JLK = 180 - 64 - 64
Angle JLK = 52degree.
Angle JLK = MLN = 52 degree (Vertical opposite angle )
M is the left over from the 2 equal angles.
N = 180 - <M - < MLN
N = 180 - 52 - 52
N = 76 degree
Hence, In the triangle LMN angle N is 76 degree.
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You can hike at an average rate of 3 miles per hour. your total hiking distance d (in miles) can be modeled by the function d = 3t where t is the time (in hours) you hike. you plan on hiking for 10 hours this weekend. what would the domain of this situation? (hint: compound inequality)
The domain of the given situation is 0≤t≤10.
Explain domainThe elements that make up a function are its domain and range. A function's domain is the set of all potential input values, while its range is the range of possible output values. Range, Function, and Domain. If a function f: A B exists that maps each element of A to an element of B, then A is the domain, and B is the co-domain. When (a, b) ∈ R, the image of element 'a' under the relation R is supplied by 'b'.
Given, the average hiking rate is 3 miles per hour.
The number of hours you plan hiking for is 10 hours.
Now, as we know that time can't be negative so we know that the domain must have t≥0.
And it is given that you plan to hike for 10 hours so the domain must also have t≤10.
Therefore, the domain of the given situation is 0≤t≤10.
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Molly has a $2500 down payment saved for this purchase. Molly assumes the $500 cash allowance will come straight off her total. How much loan does molly need?.
Answer:
Answer: $3000
Step-by-step explanation:
Based on the information given, the amount of loan that Molly needs will be the addition of the down payment and the cash allowance and this will be:
= Down payment + Cash allowance
= $2500 + $500
= $3000
Molly needs a loan of $3000
What is the slope?
A) -5/4
B) 5/4
C)-4/5
D) 4/5
Answer:
A
Step-by-step explanation:
The slope is not increasing y as x is increasing, so you immediately know the slope is negative. The formula is rise/run so the change in y/rise is 5 and the change in x/run is 4. Which allows you to get -5/4
Find the product a²b(2a³b-5ab).
Answer:
Multiply each term in the parentheses by a²b
2a⁵b²- 5a³b²
Answer:
Step-by-step explanation:
[tex]a^2b(2a^3b-5ab)=\\\\2a^3ba^2b-5aba^2b=\\\\2a^{3+2}b^{1+1}-5a^{1+2}b^{1+1}=\\\\2a^5b^2-5a^3b^2[/tex]
Can you find the slope and type the correct code? Please remember to type in ALL
CAPS with no spaces.
Puzzle #2
1: Find the slope:
XO-2
-1
79339
Your answer
-3
3 Find the slope:
2: Find the slope:
(-1, 5), (2, -7)
& Find the slope:
Y
00 00 00 0X
8
8
8
8
97233
1
4
answer choices
C:
mau
A=
B=
m
undefined m=6
D: - E
F:
m²3m=-6 m = 3
G=
H=
m = -4|m=4
I:
A
m=0
Type the 4-
letter code into
the answer
box. All CAPS.
no spaces.
Et
Answer:
The answer is -4 as the correct slope for Find the slope:
(-1, 5), (2, -7)
Step-by-step explanation:
dont guess please
Solve the equation below using the given domain, then enter the solution set. Be sure to use the {} properly and separate each entry with a comma. Finally, enter the solution set in the order that the domain is given.
Sample Answer: {(1, 2), (3 , 4), (5, 6), ...}
Equation: 2y = 6x - 10
Domain: {-1, 3, 8}
The solution set of the given equation is {(-1,-8),(3,4),(8,19)}.
Define solution set and domain.The set of ordered pairs that make up the solution to an equation with two variables is referred to as the solution set.
In mathematics, a function's domain is the collection of possible inputs it will accept.
Given equation is 2y = 6x - 10 and domain is {-1, 3, 8}
We can also write the given equation is
y =(6x-10)/2 ------------equation 1
As we know, domain is considered as the value of x,
Consequently, if we enter x = -1 in equation 1, we will receive
y = (-16)/2
y = -8
Similarly put x = 3 in equation 1, we will get
y = 8/2
y = 4
Similarly put x = 8 in equation 1, we will get
y = 38/2
y = 19
By combining the values of x and y, we get
The solution set of the given equation is {(-1,-8),(3,4),(8,19)}.
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Abigail buys 12 bottles of grapefruit juice at the corner store for a total cost of $12.48. If each bottle costs the same amount, how much is 19 bottles of juice?
The cost of 19 bottles of juice is $19.76.
What is cost per-unit rate?The "Unit Price" tells us the cost per litre, per kilogram, per pound, etc, of what we want to buy.
Given that, Abigail buys 12 bottles of grapefruit juice at the corner store for a total cost of $12.48 and each bottle costs the same amount,
Cost of one bottle = 12.48/12 = $1.04
Cost of 19 bottles = $1.04*19 = 19.76
Hence, The cost of 19 bottles of juice is $19.76.
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4. Marcella has 4 fewer male cousins than female cousins. Let f represent the number of femalecousins. Write an expression for the number of boy cousins.
Since f is the number of female cousins and the number of male cousins is 4 less than the number of female cousins, we can write the following expression to represent the number of male cousins:
[tex]f-4[/tex]For example, if the number of female cousins is 7, we can use this value (f = 7) in the expression above to find the number of male cousins:
[tex]7-4=3[/tex]So if the number of female cousins is 7, the number of male cousins is 3.
Therefore the expression for the number of boy cousins is f - 4.
Evaluate the numerical expression the quantity 2 to the power of five sixths end quantity over the quantity 2 to the power of one sixth end quantity.
cube root of 4
cube root of 2
square root of 8
square root of 6
2 is the numerical expression when 2 to the power of five sixths.
What are power and exponent?
Exponents and powers are two techniques for simplification of extremely big or extremely small numbers. For instance, we can write 3 x 3 x 3 x 3 as 34, where 4 is the exponent and 3 is the base, to demonstrate 3 x 3 x 3 x 3 in a straightforward manner. It is claimed that the entire statement 34 has power.In multiplication, a number's power indicates how many times it should be used. Other names for powers include exponents and indices.[tex]2^{5/6} * 2^{1/6}[/tex]
[tex]2^{6/6}[/tex]
2¹
= 2
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Solve by factoring64x^2-1=0
Given:
[tex]64x^2-1=0[/tex]Required:
To solve the given equation by factoring method.
Explanation:
Consider
[tex]64x^2-1=0[/tex][tex]\begin{gathered} (8x)^2-1^2=0 \\ (8x+1)(8x-1)=0 \\ \\ 8x+1=0 \\ 8x=-1 \\ x=-\frac{1}{8} \end{gathered}[/tex]And
[tex]\begin{gathered} 8x-1=0 \\ 8x=1 \\ x=\frac{1}{8} \end{gathered}[/tex]Final Answer:
[tex]x=-\frac{1}{8},\frac{1}{8}[/tex]The price of a go kart that Rafael wants to buy is $2,589 when the go kart goes on sale next month, the price will be $2,119. Which is the best estimate of the amount of money that Rafael will save if he waits to buy the go kart next month?
Current price of go-kart = $2,589
Price of go-kart next month = $2,119
If Rafael decides to buy the go-kart next month,
He will save $2,589 - $2,119 = $470
By definition of estimation
Estimation is an approximate calculation or judgment of the value, number, quantity, or extent of something
Approximating to the nearest hundred
$470 = $500
Therefore, Rafael will save an estimate of $500 if he wants to buy the go-kart next month
Towns K and L are shown on a map.
a) Work out the actual distance
between towns K and L.
b) A third town, M, is 150 km due
South of town K.
Mark M on the map with X.
c) Measure the bearing of town L
from town K.
A)The actual distance between towns K and L is 10 cm .
B) The bearing of town L from town k is 117 degree
What is mean by actual distance?The length of the line segment connecting the two sites is used to measure distance between them. The shortest line segment between a point and a line will have a length equal to the distance between them.
The following list includes four distance metrics that are maybe the most often employed in machine learning: the Hamming Distance. Distance in Euclid. New York City distance
The distance a number is from 0 on the number line is its absolute value. Because -7 is 7 units away from 0, its absolute value is 7. Because it is 5 units away from 0, the number 5 has an absolute value of 5. Any number that is less than zero is considered to be negative.
Given ,
A)The actual distance between towns K and L is 10 cm .
B) check the photo of my work
C) The bearing of town L from town k is 117 degree
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A pair of supplementary angles are in the ratio 4:5.Find the complement of smaller angle .
The complement of the smaller angle of supplementary angles in ratio 4:5 is given by 10 degree.
Given that the supplementary angles are in ratio 4:5.
Let the angles be 4x and 5x respectively.
We know that the sum of supplementary angles is 180 degree.
So, 4x+5x = 180
9x = 180
x = 180/9
x = 20
So the angles are = (20*4),(20*5) = 80,100.
So the smaller angle is 80 degree.
So the complement of the smaller angle is = 90-80 = 10 degree.
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Can I get help with question 6-9For 6 I’ve already done it I just need assistance and see if I did it correctly
The scale factor is always the ratio of new image with respect to the old image.
6) The scale factor as per the image is 3:1 or 3.
7) The New image is P'Q'R'S' and old image is PQRS so the scale factor is given by:
Q'R':QR=3:6 or 1:2.
The scale factor is 1/2.
8) Here the pair of congruent angles is:
[tex]\begin{gathered} \angle G=\angle S=90 \\ \angle F=\angle R=35 \\ \angle H=\angle T=90-35=55 \end{gathered}[/tex]The proportional sides are:
[tex]\frac{HF}{TR}=\frac{HG}{TS}=\frac{GF}{RS}=\frac{2}{1}[/tex]So FG corresponds to RS, GH corresponds to TS, HF corresponds to TR.
Padma is covering the top of her square pyramid with gold foil. If there is no overlap, how much foil will she need?Round to the nearest cm2
Answer: She will need 1239 cm^3 of foil
Explanation:
Surface area of square pyramid = base area of square + area of 4 triangular faces
Area of square base = l^2
where
l is the length of each side of the square base
From the information given,
l = 8
Area of square base = 8^2 = 64
Area of each triangular face = 1/2 x base x height
We would find the height of each face by applying Pythagorean theorem to the right triangle formed below. It is ex[ressed as
hypotenuse^2 = one leg^2 + other leg^2
hypotenuse = 10
one leg = 4
other leg = h
4^2 + h^2 = 10^2
36 + h^2 = 100
h^2 = 100 - 36 = 64
h = √64
h = 8
base = 8
Area of 4 triangular faces 4 x 1/2 x 8 x 8 = 128
Surface area of square base pyramid = 128 + 64 = 192 in^2
We would convert 192 in^2 cm^2
Recall,
1 inch^2 = 6,4516 cm^2
192 inch^2 = 192 x 6.4516
= 1239 cm^2
She will need 1239 cm^3 of foil
evaluate each sequence's related arithmetic series. 1, 2 and 3 please.
In order to evaluate the sequences, let's find the ratio of each one by subtracting the second term and the first one.
1)
[tex]\begin{gathered} 1,-5,-11,\ldots \\ r=-5-1=-6 \end{gathered}[/tex]Since the ratio is negative, the sequence is decrescent.
2)
[tex]\begin{gathered} 2.5,5.5,8.5,\ldots \\ r=5.5-2.5=3 \end{gathered}[/tex]The ratio is positive, so we have a crescent sequence.
3)
[tex]\begin{gathered} 4.7,8.7,12.7,\ldots \\ r=8.7-4.7=4 \end{gathered}[/tex]The ratio is positive, so we have a crescent sequence.
I need help with 7 please it says find the value of x round each answer to the nearest tenth
To find the value of x, we can work the two triangles separately; as follows:
So, according to the figures above:
x = y + z, and we can find y and z using Pythagoras theorem:
[tex]y\text{ = }\sqrt[]{14^2-12^2}=\text{ 2}\sqrt[]{13}[/tex][tex]z\text{ = }\sqrt[]{29^2-12^2}=\text{ }\sqrt[]{697}[/tex]Then:
[tex]x\text{ = 2}\sqrt[]{13\text{ }}+\text{ }\sqrt[]{697}=33.6[/tex]In a survey of 164 pet owners, 61 said they own a dog, and 66 said they own a cat. 11 said they own both a dog and a cat. How many owned neither a cat nor a dog?
The given information is:
- They surveied 164 pet owners
- 61 own a dog
- 66 own a cat
- 11 own both a dog and a cat
We have to find how many owned neither a cat nor a dog.
We can represent this survey in the following diagram:
To find the solution we need to subtract the number of people who said they own a dog, own a cat, and own both, from the total number of people in the survey, so:
[tex]\begin{gathered} People\text{ who own neither a dog nor a cat}=164-61-66-11 \\ P=26 \end{gathered}[/tex]The people who own neither a dog nor a cat are 26.
Amelia needs to buy some cat food. At the nearest store, 3 bags of cat food cost $13.50. How much would Amelia spend on 5 bags of cat food?
Amelia would spend $ on 5 bags of cat food.
PLEASEE HELPPP QUICK
Answer:
$22.50 for 5 bags of cat food
Step-by-step explanation:
$13.50 divided by 3 equals $4.50. Multiply this by 5 and you will end up with $22.50 for 5 bags of cat food
Dane is selling popcorn for a fundraiser. If each bag of popcorn
he sells costs $4.75, what equation can he use to calculate the
total amount of money he has raised if he has sold a number
of bags?
Answer:
Let the number of bags be 3 and the amount, x
1 bag = $4.75
1 bag = $4.753 bags = x
cross-multiply
x = $4.75 × 3
x = $14.25
hence,
3 bags = $14.25
Equation he can use:
Equation he can use:Since the amount for 1 bag is already stated, the number of bags sold is multiplied by the amount for 1 bag to get the amount.
Answer:y=4.72
Step-by-step explanation:
Jay wants to make a bike ramp a draw the following sketch what is the surface area of the ramp
We find the surface area of the figure by dividing the figure into smaller ones. This is:
Area 1, rectangle:
[tex]A=\text{length}\times width=2.2\times1.6=3.52[/tex]Area 2, triangle:
[tex]A=\frac{base\times height}{2}=\frac{2\times0.9}{2}=0.9[/tex]Area 3, rectangle:
[tex]A=1.6\times0.9=1.44[/tex]Area 4, triangle:
[tex]A=\frac{2\times0.9}{2}=0.9[/tex]Area 5, rectangle:
[tex]A=2\times1.6=3.2[/tex]Therefore, the surface area of the ramp is:
[tex]A=A1+A2+A3+A4+A5[/tex]Substitute the corresponding values:
[tex]A=3.52+0.9+1.44+0.9+3.2=9.96[/tex]Answer: 9.96 m^2
For the function f(x) = 2|5x + 7– 1, evaluate f(-4).
To evaluate f(x) at x = -4 we substiitute x in the equation with -4. Doing this gives
[tex]f(-4)=2|5(-4)+7|-1[/tex][tex]f(-4)=2|-20+7|-1[/tex][tex]\begin{gathered} f(-4)=2|-13|-1 \\ f(-4)=2\cdot13-1 \end{gathered}[/tex][tex]f(-4)=25[/tex]which is our answer!
A basketball player makes 95 out of 140 free throws. We should estimate the probability that the player makes the next free throw to be
Since the player makes 95 out of 140 free throws, the probability that he makes the next free throw is:
[tex]\frac{95}{140}\approx0.6786.[/tex]Answer: 67.86%
Can you just tell me if I did it right thank you.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question
STEP 1: Write the given equation
[tex]y=x^2[/tex]STEP 2: Complete the table
[tex]\begin{gathered} y=x^2 \\ \text{When x=x} \\ y=x^2 \\ \text{When x=}0 \\ y=0^2=0 \\ \text{When x=1} \\ y=1^2=1 \\ \text{When x=2} \\ y=2^2=4 \end{gathered}[/tex]Hence, the table for the equation will be:
what is the z value needed to conduct a two tail test in a statistical inference problem, specifying a 90% level of confidence?
the z value needed to conduct a two tail test in a statistical inference problem, specifying a 90% level of confidence is 1.65
A confidence interval is based on the sample statistics and is used to estimate a population parameter.
For example, a sample mean is used to build a confidence interval to estimate the population mean.
the z value needed to conduct a two tail test in a statistical inference problem, specifying a 90% level of confidence is 1.65
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