Answer:753
Step-by-step explanation:
The value of [tex]n^{th}[/tex] term can be calculated by,
[tex]T_{n} = a+(n-1)d\\[/tex]
where,
a = first number of the series
d = constant difference between the numbers
So, according to the question,
a = -6
d = 11
n = 70
hence, by substituting,
[tex]T_{n} = (-6)+(70-1)11\\T_{n} = 753[/tex]
Final answer:
The 70th term of the arithmetic sequence -6, 5, 16 is calculated using the formula for the nth term of an arithmetic sequence, resulting in the 70th term being 753.
Explanation:
The student is asking for the 70th term of the arithmetic sequence -6, 5, 16. In an arithmetic sequence, the difference between consecutive terms is constant. This difference is referred to as the common difference "d". The formula for finding the nth term an of an arithmetic sequence is:
an = a1 + (n - 1)d
Using the provided sequence, we can find the common difference by subtracting the first term from the second term:
d = 5 - (-6) = 11
Now, apply the formula to find the 70th term:
a70 = a1 + (70 - 1) imes d
a70 = -6 + 69 imes 11
a70 = -6 + 759
a70 = 753
Therefore, the 70th term of the given arithmetic sequence is 753.
what is -21=-7x help
Answer:
x=3
Step-by-step explanation:
-21=-7x
-7x=-21
x=3
hot air balloon is in the shape of a sphere .find the volume of a hot air balloon that is 32 ft in diameter
Answer:
Search Results
Sphere
Solve for volume
V≈17157.28
Step-by-step explanation:
The scale of a map is 1:1000. The actual dimensions of a rectangle is 4cm by 3cm. What is the actual area in m²?
(hint: convert 1000cm -> m)
(ans: 1200m²)
BUT HOW TO DO....
Step-by-step explanation:
1cm:1000cm
multiply the dimensions by 1000cm
4cm--> 4000cm
3cm--> 3000cm
convert 4000cm and 3000cm to metres by dividing by 100
because 1m=100cm
4000/100=40m
3000/100=30m
40m x 30m= 1200m²
a box of cereal weighs 600 grams . how much is this weight in pounds ? explain or show your reasoning .
Answer:
600 Grams = 1.323 Pounds
Step-by-step explanation:
1 gram equals 0.0022 pounds
600 x 0.0022 = about 1.323
Answer:
the weight in pounds is 1.324 pounds
Step-by-step explanation:
Hello, i can help you with this, you can easily solve this by using a rule of three, also you need to know
1 pound = 453 grams
Step 1
establish the relation
1 pound ⇔ 453 grams
x pound ⇔ 600 grams
the relation is
[tex]\frac{1}{453} =\frac{x}{600}\\ solve\ for\ x\\x=\frac{1*600}{453}\\x=1.324\\[/tex]
so, the weight in pounds is 1.324 pounds
I really hope It helps , have a nice day.
Whats 6x6+9-2-1=
(my mom will not let me use a calculator)
Answer:
42
Step-by-step explanation:
6*6+9-2-1
36+9-2-1
45-2-1
43-1
42
An ice cream store sells 2drinks, in 5 sizes, and 5 flavors. In how many ways can a customer order a drink?
Answer:
2*5*5= 50 because for each drink (2) there’s (5) different sizes and (5) flavors.
Step-by-step explanation:
A customer at an ice cream store can order a drink in 50 different ways by choosing from 2 drinks, 5 sizes, and 5 flavors, as calculated by the fundamental counting principle.
Explanation:To determine the number of ways a customer can order a drink at an ice cream store with 2 drinks, 5 sizes, and 5 flavors, we need to calculate the combinations of these options. Since each choice is independent of the others, we use the concept of the fundamental counting principle, where we multiply the number of options for each category together.
For drinks, there are 2 options. For sizes, there are 5 options, and for flavors, there are 5 options.
We multiply these options together: 2 drinks * 5 sizes * 5 flavors = 50 combinations.
Therefore, a customer can order a drink in 50 different ways.
Factor completely : 35 + 5x
Answer: 5(7+x) because this is how you factor
what is the surface area of a cylinder with the hight of 7 and the diameter of 9
Answer:
Step-by-step explanation:
for this, you need to remember a formula for the curved bit of the cylinder. The top and the bottom circles are easy since you only need to find their areas which are πr^2 therefore to find the radius you half 9. So 4.5^2 x π =63.62 then times two as there are two parts.
63.62 x 2 =127.24
For the curved, long bit use formula of 2πhr.
2 x π x 7 x 4.5 =63π =197.92
24 tenths minus 1 one and 3 tenths?
Answer: " 1. 1 " ; or, write as: " 1 [tex]\frac{1}{10}[/tex] " .
________________________________________________
Step-by-step explanation:
________________________________________________
(24/10) - 1 3/10 =
2 4/10 - 1 3/10 =
2.4 - 1.3 =
_______________________
2. 4
- 1. 3
___________
?
______________________________
2. 4
- 1. 3
___________
1 . 1
______________________________
The answer is: " 1. 1 " ; or, write as: " 1 [tex]\frac{1}{10}[/tex] " .
_______________________________
Please show all work cuase I don’t understand thank you
Answer:
13a. 0.92 miles
13b. C
Step-by-step explanation:
13a. The first ride costs $2.75 more than the second ride. Each quarter mile after the first quarter mile costs $0.75, so the difference in distance is:
0.75 d = 2.75
d = 3.67
The difference is 3.67 quarter miles, or 0.92 miles.
13b. The total cost is the cost of the first quarter mile plus the cost of the rest of the quarter miles.
C(n) = 2.50 + 0.75 (n − 1)
A fountain launches a stream of water directly out of a pool at a vertical speed of 48 feet per second. The water shoots up and then falls back into the pool. The height, h, of the water at time t, in seconds, is given by the equation h = –16t 2 + 48t. The greatest height of the water above the pool is
Answer:
36 feet.
Step-by-step explanation:
h = -16t² + 48t .......... (1)
The above equation relates the height h, in feet of the water at time t, in seconds.
Now, condition for greatest height is [tex]\frac{dh}{dt} = 0[/tex] ......... (2)
So, differentiating equation (1) with respect to t we get, -32t + 48 = 0 {From condition (2).
⇒ t = 1.5 seconds
So, the greatest height is = -16 (1.5)² + 48 (1.5) = 36 feet. (Answer)
Find the average rate if change in the function f(x) = x^2 +2 over the interval x= -5 to x= -2
If f(x) = x^2 +2 and 5<= x <= -2 :
F(-5)=(-5)^2+2=25+2=27
F(-4)=(-4)^2+2=16+2=18
F(-3)=(-3)^2+2=9+2=11
F(-2)=(-2)^2+2=4+2=6
Average =
(27+18+11+6)/4
=62/4
=15.5
Hope this helps
three sister are getting new outfits. shirts cost 11 each,skirts coat 25 each and shows cost 44 a pair what is the total coast of the new outfits for all of the sisters
Answer:
240.
Step-by-step explanation:
Here is the correct question: Three sister are getting new outfits. shirts cost 11 each,skirts coat 25 each and shoes cost 44 a pair. what is the total cost of the new outfits for all of the sisters?
Given: Cost of each shirt is 11
Cost of each skirts coat is 25
Cost of each pair of shoes cost is 44.
Now, finding total cost of shirt, skirt coat and shoes as cost of one new outfit.
= [tex]11+25+44 = 80[/tex]
∴ Total cost of one new outfit is 80.
Next, finding cost of new outfit for all, three sisters.
Cost of new outfit for three sister = [tex]\textrm { cost of one outfit}\times \textrm{ number of sisters}[/tex]
∴ Cost of new outfit for three sister = [tex]80\times 3= 240[/tex]
240 is the total cost of new outfit for all the sisters.
What is the image of (-9, -1) after a dilation by a scale factor of 2 centered at the
origin?
Answer:
(- 18, - 2 )
Step-by-step explanation:
Since the dilatation is centred at the origin then multiply each of the original coordinates by the scale factor for image, that is
(- 9, - 1 ) → (2 × - 9, 2 × - 1 ) → (- 18, - 2 )
Answer:
top is correct
Step-by-step explanation:
A fair coin is tossed in the air four times. If the experimental probability of landing on tails is 1/4, then what is the difference between the experimental and theoretical probability?
Answer: 1/4
Explanation:
You flipped the coin 4 times and got only one tail in those four flips. So that's where the 1/4 comes from when you state the experimental probability of tails is 1/4.
The theoretical probability of tails is 1/2 assuming it's a fair coin, as each side is likely to land on. The theoretical probability is one that can be calculated without having to do the experimental trials.
Subtract the two fractions: 1/2 - 1/4 = 2/4 - 1/4 = (2-1)/4 = 1/4
The difference between the experimental (1/4 or 0.25) and theoretical (0.5) probability of a coin landing on tails after four tosses is 0.5 - 0.25, which equals to 0.25 or 25%.
Explanation:The difference between the experimental and theoretical probability of landing on tails when a fair coin is tossed four times is sought after. The theoretical probability of a coin landing on tails is 0.5 for each toss. If a student conducts an experiment where the coin lands on tails with a probability of 1/4, we first convert this to a decimal to compare it to the theoretical value, which is 0.25.
To find the difference, subtract the experimental probability from the theoretical probability:
Theoretical Probability: 0.5 (or 1/2)
Experimental Probability: 0.25 (or 1/4)
Difference = Theoretical Probability - Experimental Probability
Difference = 0.5 - 0.25
Difference = 0.25
Thus, the difference between the experimental and theoretical probability is 0.25, or 25%.
Jon borrows $6.50 from his friends to pay for snacks, and $11.75 from his sister to go to the movies. how much money does he need to repay
Answer:
Step-by-step explanation:
You need to add $6.50 and $11.75 and you get $18.25.
Triangle A B C is shown with its exterior angles. Angle B A C is (p + 4) degrees and angle A C B is 84 degrees. Exterior angle X B C is (3 p minus 6 degrees).
What is the measure of ∠XBC?
m∠XBC = m∠BAC + m∠BCA
3p – 6 = p + 4 + 84
3p – 6 = p + 88
2p – 6 = 88
2p = 94
Answer:
The diagram of the question is attached here.
The measure of [tex]\angle XBC=135\ (deg)[/tex]
Step-by-step explanation:
All the options given here will be used to find the numeric value of [tex]\angle XBC[/tex]
Here it is shown systematically.
Exterior angle theorem: Sum of two interior angles are equal to the measure of opposite exterior angle in a triangle.
To find [tex]\angle XBC[/tex]
[tex]m\angle XBC = m\angle BAC + m\angle BCA[/tex]
Plugging the values.
[tex]3p-6 = p + 4 + (84)[/tex]
[tex]3p-6 = p + 88[/tex]
Subtracting [tex]p[/tex] both sides.
[tex]2p-6 = 88[/tex]
[tex]2p = 94[/tex]
Dividing [tex]2[/tex] both sides.
[tex]p=\frac{94}{2}=47[/tex]
So plugging the value of [tex]p=47[/tex] in [tex]3p-6[/tex] we will get the measure of [tex]\angle XBC[/tex].
So [tex]\angle XBC=(3p-6)=3(47)-6=135\ (deg)[/tex]
The measure of [tex]\angle XBC[/tex] is [tex]135\ degrees[/tex].
Based on the information, the measure of Angle XBC is 278 - 4p degrees.
What's the measurements?Given that Angle ACB is 84 degrees, Angle BAC is (p + 4) degrees, and Angle XBC is (3p - 6) degrees, you can plug in these values:
(p + 4) + 84 + (3p - 6) + Angle XBC = 360
Combine the like terms involving 'p':
4p + 82 + Angle XBC = 360
Subtract 82 from both sides:
4p + Angle XBC = 278
Now, isolate Angle XBC by subtracting 4p from both sides:
Angle XBC = 278 - 4p
So, the measure of Angle XBC is 278 - 4p degrees.
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Which expression is equivalent to (x^27y) ^1/3
Answer:
x^9*y^1/3
Step-by-step explanation:
Because x^(27*1/3)=x^9 and y^(1/3)=y^1/3.
What is the slope of this line?
15
−15
5
−5
Answer:
the slope is 1/5 which is none of these. y=1/5x+3 is the equation
Step-by-step explanation:
for every single y value that the graph goes up, it travels 5 units on the x axis.
rise over run is the way i remeber slope, rise is one for every 5 run. This has a slope of positive 1/5x.
The slope of the line is [tex]\dfrac{1}{5}[/tex]. So, the correct option is A.
Given:
The graph of the line.
To find:
The slope of the given line.
Explanation:
Slope formula: If a line passes through the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the slope of the line is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given graph it is clear that the line passes through the points [tex](0,2)[/tex] and [tex](5,3)[/tex]. So, the slope of the line is:
[tex]m=\dfrac{3-2}{5-0}[/tex]
[tex]m=\dfrac{1}{5}[/tex]
Therefore, the slope of the line is [tex]\dfrac{1}{5}[/tex] and the correct option is A.
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What is the slope of y = -4?
Answer:
The slope is 0 and the y-intercept is -4
help me solve this please
Answer:
x= -6
Step-by-step explanation:
First, you would write down the equation how it is shown first.
1) -x/3=2
Second, you would naturally multiply both sides by -3. To solve the equation, you need to use the inverse operation in the inverted order of PEMDAS. (Parentheses, exponent, multiplication, division, addition, and subtraction.)
2) -3(-x/3)=-3* 2
Lastly, you are going to reduce and simplify your new equation. This last step will achieve you your desired answer.
3) x= -6
6/3=2
Step-by-step explanation:
I know because 2×3=6 so 6/3 would have to equal 2.
Scientists have discovered a new substance with a hydrogen ion concentration of 0.095811180 M. Determine the corresponding pH level for this new substance. Round your final answer 3 decimal places
Answer: 1.018
Step-by-step explanation:
The pH level of a substance indicates the concentration of hydrogen ions ([tex]H^{+}[/tex]) in a solution and is calculated by:
[tex]pH=-log(H^{+})[/tex]
In this case the hydrogen ion concentration is [tex]0.095811180 M[/tex], where
[tex]M=\frac{moles}{volume}[/tex]. Hence:
[tex]pH=-log(0.095811180 M)[/tex]
[tex]pH=1.018[/tex] This means this new substance is acid
Which system of equations has infinitely many solutions?
A)6x + 3y = 12
3x + y = 9
B)2x + 3y = 6
4x + y = 8
C)12x +9y = 6
4x + 3y = 6
D)5x + 10y = 20
2x+4y=8
Complete the solution of the equation. Find the
value of y when x equals 24.
-2x + 2y = -56
Answer:
For x = 24, y = -4.Step-by-step explanation:
[tex]Put\ x=24\ to\ the\ equation\ -2x+2y=-56,\ and\ solve\ it\ for\ y:\\\\-2(24)+2y=-56\\\\-48+2y=-56\qquad\text{add 48 to both sides}\\\\-48+48+2y=-56+48\\\\2y=-8\qquad\text{divide both sides by 2}\\\\\dfrac{2y}{2}=\dfrac{-8}{2}\\\\y=-4[/tex]
John walks 3 miles in 5 hours
for his exercise routine. Find
the Unit rate
John walks 0.6 miles in 1 hour.
Step-by-step explanation:
Distance walked by John = 3 miles
Time period = 5 hours
5 hours = 3 miles
Unit rate is the ratio of two measurements, in which one measurement is one, therefore,
1 hour = [tex]\frac{3}{5}\ miles[/tex]
[tex]1\ hour=0.6\ miles[/tex]
John walks 0.6 miles in 1 hour.
Keywords: ratio, distance
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Choose all the examples that describe volume.
✓
A. the amount of shampoo in a bottle
✓ B. the amount of soap in a bar of soap
c. the amount of border around a chalkboard
D. the amount of wrapping paper covering a gift
Answer:
A, B
Step-by-step explanation:
Volume: the measure of the amount of space that a substance (such as liquid, gas, or solid) occupies in an enclosed environment (such as a container).
Leona purchased a $1,000 bond having a quoted price of 99.875. She had to pay a 5.5% brokerage fee (of the selling price). What was the total cost of the bond (to the nearest whole cent)?
$943.82
$1,064.44
$534.77
$2,054.22
None of these choices are correct.
The total cost of Leona's bond is $1,053.68 when accounting for the quoted price and the 5.5% brokerage fee. Consequently, the option that correctly represents the total cost is 'None of these choices are correct.'
Explanation:Leona purchased a $1,000 bond having a quoted price of 99.875. To calculate the purchase price of the bond, we multiply the face value of the bond by the quoted price percentage:
Purchase Price = Face Value × (Quoted Price / 100) = $1,000 × (99.875 / 100) = $998.75
Next, we need to calculate the brokerage fee, which is 5.5% of the selling price. We will use the purchase price to calculate this:
Brokerage Fee = Purchase Price × (Brokerage Fee Percentage / 100) = $998.75 × (5.5 / 100) = $54.93
Lastly, we add the brokerage fee to the purchase price to find the total cost of the bond:
Total Cost = Purchase Price + Brokerage Fee = $998.75 + $54.93 = $1,053.68
Therefore, Leona's total cost for the bond is $1,053.68, which to the nearest whole cent is $1,053.68. The correct answer is 'None of these choices are correct.'
Final answer:
Leona's total cost for a $1,000 bond with a quoted price of 99.875 and a 5.5% brokerage fee is $1,053.68. Option E.
Explanation:
To calculate the total cost of the bond that Leona purchased, we need to consider both the quoted price of the bond and the brokerage fee. The quoted price of the bond is 99.875% of the face value, which means the price before the brokerage fee is 99.875/100 * $1,000 = $998.75. Then, we must calculate the brokerage fee, which is 5.5% of the selling price. Therefore, the brokerage fee equals 5.5/100 * $998.75 = $54.93.
To find the total cost of the bond, we add the price of the bond to the brokerage fee: $998.75 + $54.93 = $1,053.68. Hence, the correct answer to the nearest whole cent is $1,053.68, and the given options do not list this correct amount.
(4,7) and (5,1) as an equation
Answer:
y = -6x + 31
Step-by-step explanation:
In order for us to make this an equation of the form y = mx + b we have to find the slope.
The formula for slope is rise/ run. The rise is 6 and the run is -1.
So, the slope is 6/-1 or -6.
Our equation is now: y = -6x + b
Substituting 4,7 into the equation we get 7 = -24 + b
So, b = 31.
To check out answers we substitute 5,1 in and it works.
Nancy can type 240 words in 6 minutes. How many words can she type in 1 minute?
Answer:
The answer is 40
Step-by-step explanation:
Divide 240 by 6 and you'll get 40 as your answer
Answer:
She can type 40 words in 1 minute
Step-by-step explanation:
Just do 240/6 equals 40 so that means every 1 minute is 40 words 40 words times 6 minutes is 240 words
Sofia has $1.90 worth of nickels and dimes. She has a total of 25 nickels and dimes altogether. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Sofia has. Define the variables that you use to write the system.
Answer:
The number of dimes does Sofia has is 13 , and The number of dimes does nickles does Sofia has is 12
Step-by-step explanation:
Given as :
The net worth of nickels and dimes = $ 1.90
The total number of nickles and dimes altogether = 25
Let The number of nickles that Sofia has = n
And The number of dimes that Sofia has = d
Now,
Since The value of 1 nickle = [tex]\frac{1}{20}[/tex] dollar
And The value of 1 dimes = [tex]\frac{1}{10}[/tex] dollar
So, According to question
n + d = 25 ..........1
And $ [tex]\frac{1}{20}[/tex] × n + $ [tex]\frac{1}{10}[/tex] × d = $ 1.90
Or, n + 2 d = 38 .....2
Solving Eq 1 and 2
∵ n + 2 d = 38
or, 25 - d + 2 d = 38
or, d = 38 - 25
∴ d = 13
So, The number of dimes she has = 13
And the number of nickles = n = 25 - 13
∴ n = 12
Hence The number of dimes does Sofia has is 13 , and The number of dimes does nickles does Sofia has is 12 Answer