Let daughter be x years old. Then, Shyam is (x + 28) years old.
So,
x(x + 28) = 204
=> x² + 28x = 204
=> x² + 28x - 204 = 0
=> x² - 6x + 34x - 204 = 0
=> x(x-6) + 34(x-6)
=> (x - 6) (x + 34) = 0
=> x - 6 = 0 or x + 34 = 0
=> x = 6 or x = -34
Since any age cannot be negative, daughter's age is 6 years old.
Question 1 of 40
Choose the function whose graph is given by:
Answer:
Option B
Step-by-step explanation:
The function is in the form A cos (bx)+c where A is the amplitude and B is the period. The amplitude of this function is 3 so that rules out option D. The formula for finding the period is 2pi/b so 2pi/pi/2 is 4 so that makes the period 4. The equation that matches the description is B
if the mean of x1,x2,x3 and x4 is 6 then find the mean of x1+10,x2+8,x3+16 and x4+2
Answer:
f the mean of this set is equal to 20, we can write down the below equation,
20 = (x1 + x2 +x3 + .... + x10)/10
x1 + x2 + x3 + ... x10 = 200
Then we can also write an equation for the mean of the given numbers as below,
Mean = [(x1+4) + (x2+8) + (x3+12) + .... + (x10+40)]/10
= (x1 + x2 + x3 + ... + x10 + 4 + 8 + 12 + ... + 40)/10
Then we can use above equation (1) to replace x1 + x2 + x3 + ... + x10 by 200
Mean = (200 + 4 + 8 +12 + 16 + 20 + 24 + 28 + 32 + 36 + 40)/10
= 420/10
= 42
If you remember Arithmetic Progressions you can simply add together the above number set.
If you closely look above, you can find that there is an Arithmetic Progression : 4, 8, 12, ... , 40
Here we want the addition of 10 terms. So we can use,
Sn = n/2(a+l)
S10 = 10/2(4+40)
= 220
Then you can easily get the answer,
Mean = (200 + 220)/10
= 42
Which of the following points lies on the graph of this equation?
A. (-3, 2)
B. (3, 5)
C. (3, 3)
D. (6, 8)
============================================================
Explanation:
If we plug in x = -3, then we get
y = (1/3)*x + 2
y = (1/3)*(-3) + 2
y = -1 + 2
y = 1
So the point (-3, 1) is on the line instead of (-3, 2). This rules out choice A.
Now let's try x = 3
y = (1/3)*x + 2
y = (1/3)*(3) + 2
y = 1 + 2
y = 3
We can see that (3,3) is on the line. That directs us to choice C as the final answer.
For the sake of completeness, let's try x = 6 to see what we get
y = (1/3)*x + 2
y = (1/3)*(6) + 2
y = 2 + 2
y = 4
So the point (6,4) is on the line instead of (6,8), which allows us to rule out choice D.
help please! means a lot :)
[tex]\\ \sf\longmapsto 3\dfrac{1}{3}+4\dfrac{1}{6}+5\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{10}{3}+\dfrac{25}{6}+\dfrac{11}{2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{40+50+66}{12}[/tex]
[tex]\\ \sf\longmapsto \dfrac{156}{12}[/tex]
[tex]\\ \sf\longmapsto Perimeter=11in[/tex]
Answer:
13 in.
Step-by-step explanation:
3 + 5 + 4 = 12
1/3 + 1/6 + 1/2 = 1
12 + 1 = 13
Who can help me with problem 2 you can earn 11 points
Answer:
m∠ADC = 90°
5x-5 = 90
x = 19
Step-by-step explanation:
The histogram below shows information about the weights (in kg) of all the packages Colin needs to send out today for his business. What fraction of packages weigh less than 30kg?
The fraction of packages that weigh less than 30kg is 3/8 for the given histogram.
To find the fraction of packages that weigh less than 30kg, we need to look at the histogram and count the number of packages that fall in the bins to the left of the 30kg mark.
Let's assume that w is weight.
As per the histogram, we have
0 ≤ w ≤10 : 0.55
10 < w ≤ 20 : 0.55
20 < w ≤ 30 : 1.9
So, 0 ≤ w ≤ 30.
0.55 × 2 + 1.9 = 3.
The total can be calculated as:
0.55+0.55+1.9+0.2+0.75+0.75+1.65+1.65 = 8
This means there are 8 packages that weigh less than 30kg.
Here, fraction = 3/8
Therefore, the fraction of packages that weigh less than 30kg is 3/8.
Learn more about the histograms here:
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The missing histogram is attached below.
Complete the table by determining the appropriate pair of integers whose product and sum are listed. [1 mark each]
Answer:
This shows that the required numbers are 2 and 4 for the first column
This shows that the required numbers are 3 and 7 for the third column
Hence the two numbers are -1 and -3 for the third column
Step-by-step explanation:
From the taken, we need to find two numbers whose their product will give 8, 21 and 3 and their sum will give 6, 10 and -4 respectively
If the product is 8 and sum is 6, then the required values area;
[tex]Product = (2\times 4) = 8\\Sum = (2 + 4) = 6\\[/tex]
This shows that the required numbers are 2 and 4 for the first column
Similarly for the second column;
[tex](7 \times 3) = 21\\(7 + 3) = 10[/tex]
Hence the two numbers are 7 and 3 for the second column
Similarly for the third column;
[tex](-1 \times -3) = 3\\(-1 + (-3)) = (-1-3) = -4\\[/tex]
Hence the two numbers are -1 and -3 for the second column
Which statements are true about the graph of the function f(x) = 6x – 4 + x2? Select two options.
Answer:
There is no graph.
Step-by-step explanation:
Sorry, can't help if you don't have any work shown.
Answer:
B and D
Step-by-step explanation:
A) The vertex form of the function is f(x) = (x +3)^2 -13, not the one shown.
B) The vertex is (-3, -13). True
C) The axis of symmetry is x = -3, not the one given.
D) The graph increases for x > -3. True
E) The function crosses the x-axis at about x=-6.6 and x=0.6.
Instructions: Find the measure of the indicated angle to the nearest degree.
?
33
8
Answer:
14
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp side /adj side
tan theta = 8/33
taking the inverse tan of each side
tan^-1 (tan theta) =tan^-1 (8/33)
theta = tan ^-1 (8/33)
theta =13.62699486
To the nearest degree
theta = 14
What is the value of c
Answer:
if im not mistaken its 121
Step-by-step explanation:
Answer:
99°
Step-by-step explanation:
The interior angle sum of any 5 sided polygon is 540°.
540-53 = 487 - 137 = 350 - 105 = 245- 146 = 99°
What is the inverse of the function () 2x 10?
Answer:
I assume that we want to find the inverse of the function:
f(x) = 2*x + 10
Remember that the inverse of a function f(x), is a function g(x) such that:
f( g(x) ) = g( f(x) ) = x
Because f(x) is a linear function, we can assume that g(x) will also be a linear function:
g(x) = a*x + b
let's find the values of a and b.
We will have that:
f( g(x) ) = 2*g(x) + 10 = 2*(a*x + b) + 10
And that must be equal to x, then we need to solve:
2*(a*x + b) + 10 = x
2*a*x + 2*b + 10 = x
this must be true for all values of x, so we can separate it as:
(2*a*x) + (2*b + 10) = x + 0
2*a*x = x (one equation for the terms with x)
2*b + 10 = 0
Solving these two equations we get:
2*b = -10
b = -10/2 = -5
2*a*x = x
2*a = 1
a = 1/2
Then the inverse function is:
g(x) = (1/2)*x - 5
Which is the graph of the equation?
(x-1)^2/3^2 + y^2/4^2=1
Answer: C
Step-by-step explanation:
The center is at (1,0). This eliminates all the options except for C.
what is the least number of apples that can be shared equally among either 6, 10 or 15 children
Find the least common multiple.
List the multiples of each number:
6, 12, 18, 24, 30, 36, 42
10, 20, 30, 40
15, 30, 45
The least common multiple is 30.
The answer is 30
Solve (−3) ⋅ 2
please help
Answer:
-6
Step-by-step explanation:
3*2=6
so the opposite of 6 is -6
Also a negetive times a positive is always a negetive number
Find the value of 9 in 7582.96.
9
0.9
0.09
90
ERCISE Find the standard deviation from the following set of observation 20, 25, 30, 36, 32, 43
Answer:
7.393691004
Step-by-step explanation:
7.4 is the standard deviation from the following set of observation 20, 25, 30, 36, 32, 43
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The given data set is 20, 25, 30, 36, 32, 43
Firstly we have to find the mean
Mean=20+25+30+36+32+43/6
=186/6
=31
The deviations from the mean are 20-31=-11
25-31=-6
30-31=-1
36-31=5
32-31=1
43-31=12
Using the definition of standard deviation (σ) , we have:
σ=√121+36+1+25+1+144/6
σ=√328/6
σ=√54.66=7.4
Hence, 7.4 is the standard deviation from the following set of observation 20, 25, 30, 36, 32, 43
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Can someone help me out please
Answer:
answer is
4ft * 5ft
= 20ft^2
need some help with this
Answer:
soy de ecuador p-by-step e
Last year, there were b pies baked for the bake sale. This year, there were 158 pies baked. Using b, write an expression for the total number of pies baked in the two years.
Help plsssssss
We simply add the two subtotals to get the grand total. If we knew the value of b, then we'd be able to find an actual numeric result.
For example, let's say b = 100 pies were baked last year. That would mean b+158 = 100+158 = 258 pies were made over the two year period. However, since we don't know what b is, we just leave b+158 as is.
Use your exponent rules to express as a single power, 94 ÷ 272
Answer:
3196 to the 8th power
Step-by-step explanation:
the difference is that -24 is just an integer and (-2)4 is asking you to multiply -2 by positive 4
Suppose that you work for a newly restructured automotive company with nearly 100,000 employees. You are in charge of purchasing engines from an overseas supplier. Company policy is that you purchase 500 engines each month to be placed into cars on the assembly line. Your overseas supplier of engines guarantees that no more than 0.9% of the new engines shipped to you will fail a simple electrical test. To check out the monthly shipment of the 500 engines you randomly select and test 50 of these engines, and you find that 1 is defective. Do you think that the supplier has met the guarantee
Answer:
The p-value of the test is 0.0764 > 0.05, which means that there is not enough evidence to reject the null hypothesis that the proportion is of at most 0.009, and thus we can conclude that the supplier has met the guarantee.
Step-by-step explanation:
Your overseas supplier of engines guarantees that no more than 0.9% of the new engines shipped to you will fail a simple electrical test.
At the null hypothesis, we test if the proportion is of at most 0.9% = 0.009, that is:
[tex]H_0: p \leq 0.009[/tex]
At the alternative hypothesis, we test if the proportion is of more than 0.009, that is:
[tex]H_1: p > 0.009[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.009 is tested at the null hypothesis:
This means that [tex]\mu = 0.009, \sigma = \sqrt{0.009*0.991}[/tex]
50 of these engines, and you find that 1 is defective.
This means that [tex]n = 50, X = \frac{1}{50} = 0.02[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.02 - 0.009}{\frac{\sqrt{0.009*0.991}}{\sqrt{50}}}[/tex]
[tex]z = 1.43[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.02, which is 1 subtracted by the p-value of z = 1.43.
Looking at the z-table, z = 1.43 has a p-value of 0.9236.
1 - 0.9236 = 0.0764.
The p-value of the test is 0.0764 > 0.05, which means that there is not enough evidence to reject the null hypothesis that the proportion is of at most 0.009, and thus we can conclude that the supplier has met the guarantee.
Mr. White and Co. has total profit of 6/7 million dollars. The spinning department gave a profit 1/4 of million dollars. Find the fraction of profit from other departments.
Answer: 17/28
Step-by-step explanation:
Since there is a total profit of 6/7 million dollars and the spinning department gave a profit of 1/4 million, then the profit gotten from other departments will be the fraction of profit from the spinning department subtracted from the total profit. This will be:
= 6/7 - 1/4
= 24/28 - 7/28
= 17/28
The fraction of profit from other department is 17/28.
A shopkeeper allows 15% discount on the marked price, still he manages to have 7% profit. How much high did he mark his goods above the cost price?
Answer: [tex]25.9\%[/tex]
Step-by-step explanation:
Given
Shopkeeper allows 15% discount on the marked price and still manages a profit of 7%
Suppose the marked price is [tex]x[/tex]
So, the selling price is [tex](1-0.15)x=0.85x[/tex]
Suppose the cost price is [tex]y[/tex]
[tex]\Rightarrow \dfrac{0.85x-y}{y}=7\%\\\\\Rightarrow \dfrac{0.85x}{y}-1=0.07\\\\\Rightarrow \dfrac{0.85x}{y}=1.07\\\\\Rightarrow y=\dfrac{0.85x}{1.07}\\\\\Rightarrow y=0.794x[/tex]
So, the percentage the shopkeeper marked his goods above cost price
[tex]\Rightarrow \dfrac{x-y}{y}\times 100\\\\\Rightarrow \dfrac{x-0.794x}{0.794}\times 100\\\\\Rightarrow \dfrac{0.2056}{0.794x}\times 100\\\\\Rightarrow 25.89\%\approx 25.9\%[/tex]
The mass of 5 m' of copper is 44 800 kg. Work out
the density of copper.
Help would be greatly appreciated
Answer:2/pi
Step-by-step explanation:
First, name the points. Top Left will be A, Top Right will be B, Bottom Right will be C, and Bottom Left will be D. Now, the area of ABCD is 4. Then, we have to find the area of the circle. The center to the midpoint of AB is 1. The length of the midpoint of AB to B is 1. So, using the Pythagorean Theorem, it will be 1^2 + 1^2 = 2, then it will be sqrt2. Finding the area of the circle will be easy now that we have the radius. sqrt2*sqrt2*pi = 2pi. So, it will be 4/2pi, and simplified, it will be 2/pi.
What type of number can be written as a fraction, where p and q are
integers and q is not equal to zero?
Answer:
Rational numbers can be written as a fraction where p and q are integers and q is not equal to zero
Which of the following best describes a basic postulate of Euclidean
geometry?
A. All circles measure 360°
B. All right triangles are congruent.
C. A straight line segment has a midpoint.
D. A straight line segment can be drawn between any two points.
Answer:
D. A straight line segment can be drawn between any two points.
Step-by-step explanation:
Euclid of Alexandria was famously known and regarded as the founder of geometry, as well as the father of geometry. He was born in the Mid-fourth century, BC and he specialized in the field of Mathematics. Some of his popular works in the field of Mathematics were Euclid's Elements, Euclidean algorithm and Euclidean geometry.
One of the basic postulate of Euclidean geometry is that a straight line segment can be drawn between any two points.
Others include;
I. All right angles are congruent.
II. All straight line segment is indefinitely extendable in a straight line.
How do i get X? i cant quite figure it out
Answer:
x is 90° I hope it will help you please follow me
Answer:
My answer came 78°
Step-by-step explanation:
First, B and C are alternate angles so,
71°= y (let) + 29°
Y= 42°
Then, X + 42 + 60 = 180°
X = 180 - 102
X = 78 °
Hope this helps. :)
How many distinguishable permutations for the letters in the word "reassessed" are there?
"reassessed" has a total of 10 characters, one of which (e) occurs 3 times and another (s) which occurs 4 times.
Taking each character to be distinct, there would be a total of 10! permutations. But we don't want to do that, and instead want, for instance,
rEassessEd
and
rEassessEd
to count as the same permutation. So we divide the previous total by the number of ways we can permute each set of repeated characters. For example, 3 e's can be rearranged in 3! ways.
So the total number of distinguishable permutations would be
10!/(3! × 4!) = 25,200
Calculate the next 3 terms and write the formula for the nth term for the following sequences. x, x+2, x+4,…
Answer:
Forth term = x + 6
Fifth term = x + 8
Sixth term = x + 10
Formular for nth term:
[tex]{ \tt{n _{th} = a + (n - 1)d}} \\ { \tt{{n _{th} = x + (n - 1) \times 2}}} \\ { \tt{{n _{th} =x + 2n - 2 }}}[/tex]
Answer:
Hello,
Step-by-step explanation:
First term of this aritmetical sequence is x+0*2
[tex]U_1=x+0*2\\U_2=x+2=x+1*2\\U_3=x+4=x+2*2\\U_4=x+6=x+3*2\\\\n^{th}\ term\ is\ U_n=x+(n-1)*2\\[/tex]
