Answer: Kate = 40/3 Her father = 50
Step-by-step explanation:
Let Kate's age in the present be K
And Kate's father's age in the present be F
3(K+5) = F+5
6(K-6) = F-6
Rearrange the first equation to get
3K+15 = F+5
3K+10 = F
Substitute that into the second question
6K-36 = 3K+10-6
3K = 40
K = 40/3
So F = 3*40/3+10 = 50
Can someone please help me with this? 1-4 thank you so much.
Answer:
1.) Option C
2.) Option B
3.) Option D
4.) Option A
Step-by-step explanation:
[tex] \frac{3x {}^{2} }{y {}^{ - 3} } \\ [/tex]
Here, we know that
[tex]a {}^{ - 1} = \frac{1}{a} \\ [/tex]
So,
[tex] \frac{ {3x}^{2} }{y {}^{ - 3} } = \frac{ {3x}^{2} }{ \frac{1}{y {}^{ 3} } } = {3x}^{2} y { }^{3} \\ [/tex]
Thus, Option C is correct
2.)[tex]( {4}^{0} )( {4}^{2} ) \\ [/tex]
We know that,
n⁰ = 1
where, n = any real number
So,
[tex]( {4}^{0} )(4 {}^{2} ) = 1 \times 16 = 16 \\ [/tex]
Thus, The answer is 16
3.)[tex]( \frac{5}{3} ) {}^{ - 3} \\ [/tex]
We know that
[tex]a {}^{ - 1} = \frac{1}{a} \\ [/tex]
So,
[tex]( { \frac{5}{3} )}^{ - 3} = ( { \frac{3}{5} )}^{3} = \frac{27}{125} \\ [/tex]
Thus, Option D is correct
4.)[tex] \frac{a {}^{2} {b}^{5}c {}^{0} }{ab {}^{7} } \\ [/tex]
[tex] \frac{a {}^{2} {b}^{5} c {}^{0} }{ab {}^{7} } = \frac{a}{ {b}^{2} } \\ [/tex]
Thus, Option A is correct
-TheUnknownScientist 72
Someone help me please
Step-by-step explanation:
the ratio of 1/18 simply means that 1 inch in the drawing represents 18 inches in reality.
so, the real flag is therefore
2×18 = 36 inches long and 1×18 = 18 inches wide (or high).
the area of the actual flag is therefore
36 × 18 = 648 in²
Find DE.
F) 3
G) 6
H) 9
J) 12
Answer:
Step-by-step explanation:
F because im guessing and im taking a tes
iready about presents plz help 7 grade lvl
Answer:
Answer:
118
Step-by-step explanation:
150+16%=174
174 - 32% = 118.32
118.32=118(to nearest whole number)
Is the cost proportional to the bags of salad?
Are the ratios of salad to cost equal?
Answer:
yes cost is proportional and ratios of cost are equal
Step-by-step explanation:
what is -3/4(2/3 in simplest form
Answer:
-1/2 or the decimal form -0.5
A bag contains 7 green marbles, 2 white marbles, 5 orange marbles, 9 green marbles, and 7 red marbles. A marble will be drawn from the bag and replaced 180 times. What is a reasonable prediction for the number of times a white or red marble will be drawn?.
Prediction for some count is usually expressible as expectation of some random variable. The reasonable prediction for the number of times a white or red marble will be drawn is 54
What does the expectation of a random variable tells about?A random variable is usually taking some numerical information of each elementary event of the sample space . (map from sample space to real numbers). Its expected value is the best prediction value in most of the cases.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
For the given case, as the ball being drawn is being replaced too, so we can take all 180 experiments to be independent from each other.
If we call
Success = Event of drawing white or red marble
Failure = Event of drawing any other marble instead of white or red
Then, each marble drawing event is having two outcomes: success or failure. This makes each drawing a Bernoulli experiment.
Modelling this situation with binomial distribution would be good.
Let X = number of successes in those 180 experiments.
P(Success) = 9/30 = 0.3 = p(say) (total 9 marbles in favor, so 9 ways of drawing single marble, and total 30 marbles are there, and thus 30 ways of drawing single marble out of them)P(Failure) = P(Not success) = 1-p = 0.7 = q (say)Thus, we get
[tex]X \sim B(n = 180, p= 0.3)[/tex]
The expectation of random variable X is the best prediction of count of times we will get in those 180 trials.
The expectation of a random variable is: [tex]E(X) = np[/tex]
Thus, we get:
[tex]E(X) = 180 \times 0.3 = 54[/tex]
Thus, the reasonable prediction for the number of times a white or red marble will be drawn is 54
Learn more about binomial distribution here:
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Megan found a new knitting pattern she's been wanting to try. It makes a rainbow-striped 60-inch scarf. Last month, it took her 14 hours to knit her little sister a 30-inch scarf. If Megan plans to knit 1 hour every day, how many weeks will it take her to finish the rainbow-striped scarf?
Answer:
if it took her 14 hours to make a 30-inch scarf, we can assume it will take her to double that time to make a 60-inch scarf. 28 hours is double of 14, if she only knits one hour every day it will take her 4 weeks, 28 days is equal to exactly 4 weeks 28/7=4 weeks
Answer:
4 weeks
Step-by-step explanation:
14 hours for a 30-inch
multiply them both by 2
28 hours for 60-inch
28 divided by 7 = 4
Have a blessed and great day<3
what is the answer to −7x>10 simplified?
Answer:
x>-10/7 or ≈ -1.4285714285714285714285714285714
Step-by-step explanation:
transfer the -7 coefficient over to the right
Hey there!
-7x > 10
DIVIDE -7 to BOTH SIDES
-7x/-7 > 10/-7
CANCEL out; -7/-7 because it give you 1
KEEP: 10/-7 because it give you the x value
NEW EQUATION: x = 10/-7
SIMPLIFY IT!
x = - 10/7 OR x = -1 3/7
⇡ EITHER OF THOSE SHOULD WORK BECAUSE THEY ARE EQUIVALENT TO EACH OTHER! ⇡
It is an OPEN circle shaded to the left starting between -1 & -2. (Little over -1)
Therefore, your answer is:
x = - 10/7 OR x = -1 3/7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
fine the GCF of these three expressions 14x , 49x , and 28
Answer:
GCF = 7
Step-by-step explanation:
7 * 2 = 14
7 * 7 = 49
4*7 = 28
[RevyBreeze]
What are these in scientific notations?
Answer:
.071 times 101
Step-by-step explanation: The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.
Given the functions f(n) = 25 and g(n) = 3(n − 1), combine them to create an arithmetic sequence, an, and solve for the 12th term. An = 25 − 3(n − 1); a12 = −11 an = 25 − 3(n − 1); a12 = −8 an = 25 3(n − 1); a12 = 58 an = 25 3(n − 1); a12 = 61.
Arithmetic sequence is done by adding or subtracting the difference. The 12th term of the arithmetic sequence will be 58.
What is the arithmetic sequence?The arithmetic sequence is the series of numbers where every two consecutive terms have the same difference between them.
We know that the nth term of an arithmetic sequence is given as,
[tex]a_n = a_1 + (n-1)d[/tex]
Also, we are given two functions adding the two functions we get,
[tex]f(x) + g(x)\\\\ = 25 + 3(n-1)[/tex]
comparing the sum we get with the arithmetic sequence formula for nth term, we will understand that,
[tex]a_1 + d(n-1)\\25+3(n-1)[/tex]
therefore,
a₁ = 25
and d = 3
that means the first term of the sequence is 25 while the difference between the two terms is 3.
Now, substituting the values in the formula we will get that the 12th terms of the sequence can be written as,
[tex]a_n = a_1 + (n-1)d\\\\a_{12} = 25 + (12-1)3\\\\a_{12} = 25 + 33\\\\a_{12} = 58[/tex]
Hence, the 12th term of the arithmetic sequence will be 58.
Learn more about Arithmetic Sequence:
https://brainly.com/question/16130064
What is the solution to 8√3 - 7√3?
√3
56√3
√6
√9
Answer:
[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Since the value under the square root is the same, you only subtract the coefficients, and you do not show the one in your final answer.
At a school carnival, the diameter of the mat of a trampoline is 16 feet and the diameter of its metal frame is 18 feet. What is the length, in feet, of the metal frame that surrounds the trampoline? Use 3. 14 for π and round your answer to the nearest tenth. 50. 2 feet 56. 5 feet 100. 5 feet 113. 0 feet.
Answer:
(b) 56.5 ft
Step-by-step explanation:
The circumference of a circle of diameter d is given by ...
C = πd
For the given diameter, the circumference of the frame is ...
C = (3.14)(18 ft) ≈ 56.52 ft
The length of the outside edge of the frame is about 56.5 feet.
Simplify the following polynomial expression.
(5x^4 - 9x^3 + 7x - 1) + (-8x^4 +
4x^2– 3x + 2) - (-4x^3 + 5x - 1)(2x -7)
A 5x^4 - 37x^3 - 6x^2 + 41x - 6
B. 11x^4- 21x^3 + 14x^2 + 33x-8
C. 11x^4- 21x^3 + 14x^2 + 33x- 6
D. 5x^4– 37x^3- 6x^2 + 4x - 8
Answer:
A. [tex]5x^4 - 37x^3 - 6x^2 + 41x - 6[/tex]
step-by-step-explanation:
[tex](5x^4 - 9x^3 + 7x - 1) + (-8x^4 +4x^2- 3x + 2) - (-4x^3 + 5x - 1)(2x -7)[/tex][tex](5x^4 - 9x^3 + 7x - 1) -8x^4 +4x^2- 3x + 2 - (-8x^4+28x^3+10x^2-37x+7)[/tex][tex]5x^4 - 9x^3 + 7x - 1-8x^4 +4x^2- 3x + 2 +8x^4-28x^3-10x^2+37x-7[/tex][tex]5x^4 -8x^4 + 8x^4 -9x^3 -28x^3 +4x^2 -10x^2 +37x +7x -3x -7 -1 +2[/tex][tex]5x^4 - 37x^3 - 6x^2 + 41x - 6[/tex]Answer:
[tex]5x^4- 37x^3-6x^2+ 41x-6[/tex]
Step-by-step explanation:
simplify the following expression:
[tex](5x^4 - 9x^3 + 7x - 1) + (-8x^4 +4x^2-3x + 2) - (-4x^3 + 5x - 1)(2x -7)[/tex]
Expand [tex](-4x^3 + 5x - 1)(2x -7)[/tex]
[tex]\implies -8x^4 +28x^3+10x^2-35x-2x+7\\\\\implies -8x^4 +28x^3+10x^2-37x+7\\[/tex]
Therefore:
[tex](5x^4 - 9x^3 + 7x - 1) + (-8x^4 +4x^2- 3x + 2)-(-8x^4 +28x^3+10x^2-37x+7)[/tex]
Group and combine like terms:
[tex]5x^4 -8x^4- 9x^3 +4x^2+ 7x - 3x- 1 + 2-(-8x^4 +28x^3+10x^2-37x+7)\\\\\implies -3x^4- 9x^3 +4x^2+ 4x +1-(-8x^4 +28x^3+10x^2-37x+7)[/tex]
Apply the distributive rule: [tex]-(-a+b)=a-b[/tex]
[tex]\implies -3x^4- 9x^3 +4x^2+ 4x +1+8x^4-28x^3-10x^2+37x-7[/tex]
Group and combine like terms:
[tex]\implies -3x^4+8x^4- 9x^3 -28x^3+4x^2-10x^2+ 4x+37x +1-7\\\\\implies 5x^4- 37x^3-6x^2+ 41x-6[/tex]
The amount of time it takes for an ice cube to melt varies inversely to the
air temperature, in degrees. At 70°F the ice will melt in 20 min. How long
vill it take the ice to melt if the temperature is 85°F?
Answer:
Time goes down to 16.47 min
Step-by-step explanation:
Formula
Time to melt = k / Temperature (I doubt it is this simple)
Givens
Temp = 70
Time = 20
k =
Solution
20 = k / 70 Multiply both sides by 70
20*70 = k
k = 1400
Problem
What happens when Temp = 85?
Time = k / Temp
Time = 1400 / 85
Time = 16.47 Min
Learn-a-Lot Academy needs to order 900 pencils for its students. The pencils come in cases of 24 boxes with 12 pencils in each box. The pencil manufacturer will sell only whole cases. How many cases of pencils must Learn-a-Lot Academy order?
Answer:
4 Cases
Step-by-step explanation:
If they bought 3 cases they would only have 864
Answer:
4 cases
Step-by-step explanation:
Find out how many pencils per case:
1 case = 24 boxes
1 box = 12 pencils
1 case = 24•12 = 288 pencils
Divide the amount of needed pencils (900) by how many per case there are (288) to find how many cases you need:
900÷288=3.125 (or 3 1/8)
Since you can't get a part of a case (for the 1/8 of a case you need), you will need to round up to 4 cases.
Find the 45th term of the below arithmetic sequence.
-9, -2, 5, 12, ...
Answer:
Check the attachment.
Hope it helps ⚜
6
—-
math
pls help geniuses!!
——
Answer:
- B
x = 9
y = 3
how do I solve this?
Value of [tex]x[/tex]is [tex] - 12[/tex].
Final Answer is [tex]480[/tex]
Step-by-step explanation:
Assume that:
First number = x
Second number = 20 - x
Putting the given conditions,
[tex]2x^{2} + 3(20 - x)^{2} [/tex]
Putting the formula (a-b)²=(a²+2ab+b²) in (20-x)²,
[tex]2 {x}^{2} + 3(20^{2} - 2 \times 20 \times x + {x}^{2})[/tex]
[tex] = > 2 {x}^{2} + 3(400 - 40x + x^{2})[/tex]
Opening the brackets,
[tex]2 {x}^{2} + 3 \times 400 - 3 \times 40x + 3 \times {x}^{2} [/tex]
[tex] = > 2 {x}^{2} - 1200 - 120x + 3{x}^{2}[/tex]
[tex] = > (2x^{2} + 3 {x}^{2}) - 120x + 1200[/tex]
[tex] = > 5 {x}^{2} - 120x + 1200[/tex]
[tex]As \: x= - \frac{b}{2a}[/tex]
[tex] = > - \frac{120}{2 \times 5}[/tex]
[tex] = > - \frac{120}{10} [/tex]
[tex] = > - 12[/tex]
Now substituting the value of x in 5x²-120x+1200,
[tex] = > (5 \times {12}^{2} )-(120 \times 12)+1200[/tex]
[tex] = > (5 \times 144)-(1440)+1200[/tex]
[tex] = > 720 - 1440 + 1200[/tex]
[tex] = > 720 - (1440 - 1200)[/tex]
[tex] = > 720 - 240[/tex]
[tex] = > 480[/tex]
Are you clever enough to earn 100 points?
What would be the answer on the graph?
Answer:
(8, 9) and (12, 3)
Step-by-step explanation:
The ends of the line would be (8, 9) and (12, 3)
Because the scale factor is negative, the guide lines go through the centre of enlargement rather than from it.
I need help with math here is the pic of the ?
Answer:
40
Step-by-step explanation:
140/100 = 56/x
=> x = (100x56)/140 = 40
Answer:
40
Step-by-step explanation:
140% x __ = 56
140/100 x __ = 56
x = 56 x 140/100
x = 40
What is the measure of∠ABC?
Answer:
95
Step-by-step explanation:
the interior angles of a square add upto 360
and from the arrows we know that the parallel sides are equal
so there will be two angles which are 85
so:
360-85-85 = 190
190/2 = 95
8. Sergei is buying tomatoes and finds that two different kinds are weighed in grams and
ounces. Tomato A is 6 ounces and Tomato B is 173 grams. Which tomato weighs the
most? (1 oz =
28.3 g)
Answer:
tomato B weighs more than tomato A
Step-by-step explanation:
Tomato A: 6oz = 169.8g
Tomato B: 6.10oz = 173g
What is the Lowest Common Multiple of 42 and 90
Answer:
630
Step-by-step explanation:
Answer:
630
Step-by-step explanation:
90/6=15
42/6=7
Those are the lowest you can go in those numbers and when you do 90*42
it is 3780. Divide that by 6 and it is 630.
Max has 40/100 of a dollar. Ben has 2/10 of a dollar. Alex has 3/10 of a dollar. Together, what fraction of a dollar do they have?
Mark all correct answers.
Group of answer choices
A.45/100
B.9/10
C.90/100
D.72/100
Answer:
b and c are correct
Step-by-step explanation:
Hope this helps! :)
Answer:
B
Step-by-step explanation:
Because max has 40/100 of a dollar which could = 4 or 40% so he has 4.
Max=4
Ben has 2/10 of a dollar which could be 2 or 20% so ben has 2
Ben=2
Alex has 3/10 of a dollar which could be 3 or 30% so Alex has 3.
Alex=3
4+2+3=9/10
Hope it helps,have a great day:)
80 points for this! please help
Answer:
it is 800.00
Step-by-step explanation:
i did this a while ago
10 points + brainliest to first correect answer :) incorrect answers/ answers with no effort will be deleted this is easy im just making sure :)
The temperature in Mariah’s town was 5.2 degrees Fahrenheit at midnight. The temperature decreased at a steady rate of 1.1 degrees Fahrenheit per hour until 7:00 a.m. From 7:00 a.m. through noon, the temperature increased by a total of 4.9 degrees Fahrenheit. What was the temperature at noon?
a- Negative 7.4 degrees Fahrenheit
b- Negative 2.5 degrees Fahrenheit
c- 2.4 degrees Fahrenheit
d- 7.4 degrees Fahrenheit
Answer:
C. 2.4 degrees Fahrenheit
Step-by-step explanation:
1.1 per hour for 7 hours
1.1 x 7 = 7.7
5.2 - 7.7= -2.5
-2.5 + 4.9 = 2.4
Evaluate 13|−x+4|−6 when x = 13.
Answer:
-123
Step-by-step explanation:
13(-x+4)-6 when .x is 13
we just replace x with 13
13(-13+4)-6
13(-9)-6
applying bodmas we multiply 13 by negative 9 before the subtraction aspect
13*-9=-117
-117-6=-123
Marina can bicycle 19. 5 miles in the same time it takes her to run 6 miles. She bikes 9 miles per hour faster than she runs. At what speed does Marina run?.
Speed is the rate at which a body changes its position. The speed by which Marina runs is 4 miles/ hr.
What is Speed?Speed is the rate at which a body changes its position. It is given by the formula,
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Given to us
Marina can bicycle 19. 5 miles at the same time it takes her to run 6 miles.
Marina bikes 9 miles per hour faster than she runs.
Let the speed of the Marina running be s, and the time is taken to run 6 miles be t.
Time is taken by Marina to cover a distance of 6 miles by running,
[tex]\rm t = \dfrac{6\ miles}{s}[/tex]
Since the speed of Marina's bicycle is 9 miles per hour faster than she runs. Time is taken by Marina to cover a distance of 19. 5 miles by bicycle,
[tex]\rm t = \dfrac{19.5\ miles}{s+9}[/tex]
We know that Marina can bicycle 19. 5 miles at the same time it takes her to run 6 miles. therefore,
[tex]\rm t = \dfrac{6\ miles}{s}= \dfrac{19.5\ miles}{s+9}[/tex]
[tex]\dfrac{6}{s}= \dfrac{19.5}{s+9}[/tex]
Solving the given equation we will get,
[tex]\rm s = 4\ miles/hr[/tex]
Hence, the speed by which Marina runs is 4 miles/ hr.
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