The value (i) 0.56, (ii) 0.81 and (iii) 200
To solve this problem, we have to use a concept known as difference of two squares.
Difference of Two Squaresa)
Given two decimals and we are to find the difference between their squares,
[tex]0.9^2 - 0.5^2\\(\frac{9}{10})^2 - (\frac{1}{2})^2 = \\ \frac{81}{100} - \frac{1}{4} = \frac{81 - 25}{100} = \frac{56}{100} = \frac{14}{25} = 0.56[/tex]
b)
We have two decimals
[tex]1.5^2 - 1.2^2 = 2.25 - 1.44 = 0.81[/tex]
c)
We would find the difference of two squares here
[tex]100.5^2 - 99.5^2 = 200[/tex]
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Graph the inequality in the coordinate plane. y<-3
Answer:
Step-by-step explanation:
Y is a horizontal line intersecting (0, -3).
Mbali walks to the lake every third day. Nqabisa walks to the lake every
fourth day. Calculate how often they will walk to the lake on the same day
Step-by-step explanation:
we need to find the LCM, the least (or lowest) common multiple, of 3 and 4.
that means the smallest number that can be divided by 3 and by 4 without remainder.
and that is simply in our case 3×4 = 12.
so, every 12th day they will walk to the lake "together" (on the same day).
FYI - formality the LCM is found e.g. by prime factorization.
starting with the smallest prime number (2) both numbers are divided by the prime number, if there is no remainder. the quotient is then again divided by the prime number. if there is a remainder, then the next higher prime number is taken for the division.
this goes on until we get a quotient of 1.
the LCM is then the product of the longest streaks of the products of the same prime numbers.
example LCM of 56 and 50
56 ÷ 2 = 28 (0 remainder)
28 ÷ 2 = 14 (0 remainder)
14 ÷ 2 = 7 (0 remainder)
7 ÷ 2 has a remainder, so the next prime number (3)
7 ÷ 3 has a remainder, so the next prime number (5)
7 ÷ 5 has a remainder, so the next prime number (7)
7 ÷ 7 = 1 finished
50 ÷ 2 = 25 (0 remainder)
25 ÷ 2 has a remainder, so the next prime number (3)
25 ÷ 3 has a remainder, so the next prime number (5)
25 ÷ 5 = 5 (0 remainder)
5 ÷ 5 = 1 finished
the longest streaks of prime number products :
2×2×2 = 8
5×5 = 25
7 = 7
the LCM = 8×25×7 = 1400
please consider, this is NOT 56×50 = 2800.
the LCM is not automatically just the product of both numbers. this product is a common multiple, true, but not always the smallest.
in our case here with 3 and 4
3 ÷ 2 has a remainder, so the next prime number (3)
3 ÷ 3 = 1 finished
4 ÷ 2 = 2 (0 remainder)
2 ÷ 2 = 1 finished
the longest prime number product streaks :
2×2 = 4
3 = 3
the LCM = 4×3 = 12
so, in this case the LCM is the direct product of both numbers.
Please help I don’t know what to do
Write a numerical expression for the phrase.
The sum of - 1 and 2 and 4
Answer:
you are adding 1 , 2 and 4 and you answer is 7
Help anyone please !!!
Answer:
Itsb
Step-by-step explanation:
Look at this set of ordered pairs:
(17, -16)
(17, 19)
(7, 16)
Is this relation a function? yes or no?
Answer:
No
Step-by-step explanation:
The input 17 has 2 different outputs
This lesson discusses inverses of trig functions. List two actions that are inverses of each other and explain how one action "undoes" the other.
Two actions that are inverses of each other are cos and arccos.
What is the trigonometric ratio?
Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.
Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.
1. Trigonometric function:
cos (π) = -1
2. Inverse function :
π = arccos( -1 )
We can see that the inverse function of "cos" is "arccos" and viceversa
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This claim is to be investigated at .01 levels. “Forty percent or more of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job were available. “Seventy-four persons out of the 200 sampled said they would return to work
- State the null hypothesis.
- What is the decision rule?
- Compute the value of the test statistic.
According to the described situation, we have that:
The null hypothesis is [tex]H_0: p < 0.4[/tex]The decision rule is:
z < 2.327: Do not reject the null hypothesis.z > 2.327: Reject the null hypothesis.The value of the test statistic is of z = -0.866.
What is the null hypothesis?The claim is:
"Forty percent or more of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job were available"
At the null hypothesis, we consider that the claim is false, that is, the proportion is of less than 40%, hence:
[tex]H_0: p < 0.4[/tex]
What is the decision rule?We have a right-tailed test, as we are testing if a proportion is less/greater than a value. Since we are working with a proportion, the z-distribution is used.
Using a z-distribution calculator, the critical value for a right-tailed test with a significance level of 0.01 is of z = 2.327, hence, the decision rule is:
z < 2.327: Do not reject the null hypothesis.z > 2.327: Reject the null hypothesis.What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In this problem, the parameters are:
[tex]p = 0.4, n = 200, \overline{p} = \frac{74}{200} = 0.37[/tex]
Hence:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.37 - 0.4}{\sqrt{\frac{0.4(0.6)}{200}}}[/tex]
[tex]z = -0.866[/tex]
The value of the test statistic is of z = -0.866.
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True or False? When adding two vectors in magnitude-direction form, we add the magnitudes together and add the direction angles together to find our resultant vector.
Answer:
True
Step-by-step explanation:
The resultant is the vector sum of two or more vectors. It is the result of adding two or more vectors together.
Answer:
The answer is true
Step-by-step explanation:
If we add the same two vectors in a different order it will still give the same resultant vector.
Find the area of the shape shown below.
Answer:
I believe a=22
Step-by-step explanation:
a=4+4+4+2+8
a=8+4+2+8
a=12+2+8
a=14+8
a=22
Round to the nearest dollar.
$7,562.36
Answer:
the answer should be $7,562.00
A small town surveyed 250 adults, 180 of whom were parents, about whether a park should be expanded. The results showed that 150 of the adults who were parents and 40 of the adults who were not parents thought the park should be expanded.
Use this information to complete the two-way table.
Enter your answer by filling in the boxes to complete the table.
Should the park be expanded?
Yes No
Parents
Not parents
Answer:
Yes, the park should be expanded
Explanation:
180 adults said yes.
250 - 180 = 70
70 people thought the park shouldn't be expanded, but there are more people who want the mark to expand.
A + b= s + r solve for r
Answer:
A + b - s = r
Step-by-step explanation:
get r alone on one side of the equal sign by subtracting s from both sides
Which best describes a cone?
Answer:A cone is a 3-dimensional solid object that has a circular base and a single vertex
Step-by-step explanation:
dolphinsproduction on insta
Answer:
A cone have a point a the top with a round end which is a circle at the bottom.
A year ago the dialy sales of newpaper averages at 16:320 now the average sales are at 28,560 express the ratio of present sales to the last year sales in the simplest form
Answer:
The ratio of present sales to last year's sales is 28560
16320.
Reducing (canceling) the factor 80*17*3 = 4080 in the numerator and denominator, you get the fraction
equal to 7 which is the simplest form.
4
Step-by-step explanation:
Which angle has a cosine of 3/5?
angle A
angle B
angle C
Cannot be determined
50 pts
Answer:
angle A
Step-by-step explanation:
cosine(θ) = adjacent/hypotenuseHere the hypotenuse is 10 and adjacent is 6.where the line of hypotenuse and adjacent meets, that angle shall falls under cosine rule.Therefore angle A has a cosine of 3/5
What is the meanng of Pi?
Answer:
The circumference of a circle is divided by the diameter of that circle. PI
Step-by-step explanation:
Hope this helps you!!!! :D
Find the missing values in the ratio table. Then write equivalent ratios. PLS help me
Answer: Find the missing values in the ratio table. Then write equivalent ratios. PLS help me
Step-by-step explanation:
I cant see the work
I have till 6 before she grades all assignments for good please help (putting this w all questions) personally i’m shaking please help ..
Hi! Refer to the graph attached below
Answer and Step-by-step explanation:
My response is in the image attached below, I hope that this helps. Good luck with your work.
PLEASE HELP ME WITH MATHHH
Answer:
A: four right angles
Step-by-step explanation:
Answer:
Four Right Angles
Step-by-step explanation:
right angles are 90°
I mean if you change the angle just a little bit of any part of a rectangle it will stop being a rectangle and it will become a quadrilateral.
Please do help me i dont understand at all
We have to use the exponent laws to figure this out. When we are multiplying a number with the same bases, we just simply add the exponents. So it would look something like this:
[tex]=11^{8\ +\ -7\ +\ 3}[/tex]
eight plus negative seven equals one, plus three equals four.
So the simplified form will be 11⁴
a = 11
n = 4
What is the volume (in cubic units) of a cylinder with a radius of 3 units and a height of 12 units? π = 3.14
Answer:
Volume is 339.12 cubic units
Step-by-step explanation:
[tex]{ \tt{volume = \pi {r}^{2} h}}[/tex]
» r is radius
» h is height
[tex]{ \tt{v = 3.14 \times ( {3)}^{2} \times (12)}} \\ { \tt{v = 3.14 \times 108}} \\ { \underline{ \tt{ \: \: v = 339.12 \: \: units {}^{3} } \: \: }}[/tex]
Pls help asap also sorry for the blurry mess…
Answer:
so 320 employees and 40% chose pink! 40% of 320 is 128!
PLS HELP ME WITH THIS IM GOING TO LOSE THE YEAR!!
Answer:
i think it would be x = $10 + $1.50 + $3.00 * 4
and B 4x = $14.50
Step-by-step explanation:
im not completely sure of this sorry if its wrong
if angle A and angle B are vertical angles. if angle A = (8x – 4)º and angle B = (7x + 3)º,
then find the measure of B
What is the value of the function y = 2x - 3 when x = -5
Answer:
y= -13
Step-by-step explanation:
2 times -5 = -10 - 3 = -13
please help me with this question. i would really appreciate it!
Answer:
it should be c or d
Step-by-step explanation:
Taiya invests $4,848 in a savings account with an interest rate of 5% compounded annually. What is the interest that she earned? *
Answer:
the answer is $6520.02
Step-by-step explanation:
explanation linked as image
Five times a number, added to the sum of the number and 3. *
A number multiplied by negative seven, subtracted from the sum of 13 and six times the number. *
i need it in a math expression please
Answer:
The first one is: 5x (x+3)
second one: 6x+13-(-7x)
Step-by-step explanation:
Sam has 6 shells.
Isabel has || shells.
Which equation can be used
to solve the problem?
Click or tap the equation.
How many shells do Sam and Isabel have in all?
IL - 6 =
6 + Il
6+
|
5 + 6 =
6 + 11 =
Step-by-step explanation:
