Answer:
12 black countersStep-by-step explanation:
Let the yellow counters be represented by 'y' and black counters by 'b'.
Originally
y : b = 3 : 1After removing 21 counters
y - 21 : b = 5 : 4Taking the first ratio, equate it to b.
y/b = 3b = y/3Now, substitute for 'b' in the second ratio.
y - 21 / (y/3) = 5/43 (y - 21) / y = 5/412 (y - 21) = 5y12y - 252 = 5y7y = 252y = 36 yellow countersNow, to find b :
b = y/3b = 36/3b = 12 black countersAnswer:
12
Step-by-step explanation:
Given ratio
yellow : black = 3 : 1
⇒ yellow : black = [tex]3x : x[/tex]
If 21 yellow counters are removed and the ratio becomes 5 : 4
[tex]\implies \textsf{yellow - 21: black = 5 : 4}[/tex]
[tex]\implies (3x - 21):x=5:4[/tex]
[tex]\implies \dfrac{3x - 21}{x}=\dfrac54[/tex]
[tex]\implies 4(3x - 21)=5x[/tex]
[tex]\implies 12x-84=5x[/tex]
[tex]\implies7x=84[/tex]
[tex]\implies x=12[/tex]
Substituting [tex]x=12[/tex] into the original ratio:
[tex]\implies \textsf{yellow : black} =3(12) : (12)=36:12[/tex]
So the total number of black counters = 12
Find the area of the circle shown.
Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
radius is 1.5 cm
Answer:
7.1 cm^2
Step-by-step explanation:
Area = pie * radius^2
Area = pie * 1.5^2
= 7.0685
Answer: 7.1 cm ^2
Step-by-step explanation:
I NEED HELP WITH NUMBER 7
Answer:
c po
because that is the answer in the bakc of my module hope its help
A straight waterslide is 175 feet above ground and is 200 feet long. What is the angle of depression to the bottom of the slide?
Step-by-step explanation:
see this this will help you
A cylinder and its dimensions are shown in the diagram. Which equation can be used to find V, the volume of the cylinder in cubic centimeter? I think A. is the answer :)
Answer: it’s simply a
Step-by-step explanation: X =bsquare
FIND THE RADIUS OF THE SHPERE WITH THE GIVEN VOLUME?
562.5π in.³
Answer:
Radius = 7.5 inStep-by-step explanation:
In the question we have given volume of Sphere that is 562.5 π in³ and we have asked to find the radius of given sphere. We know that the volume of sphere ,
[tex] \blue{ \boxed{ \rm{Volume \: of \: Sphere = \frac{4}{3} \pi r {}^{3} }}}[/tex]
So equating it with given volume for finding the radius of sphere :
[tex] \longmapsto \: \frac{4}{3} \pi r{}^{3} = 562.5\pi[/tex]
Step 1 : Cancelling π as it was present in both side :
[tex]\longmapsto\:\frac{4}{3} \cancel{\pi }r{}^{3} = 562.5 \cancel{\pi}[/tex]
Step 2 : Transposing 4/3 to right hand side :
[tex]\longmapsto \: r {}^{3} = 562.5 \times \frac{3}{4} [/tex]
Step 3 : Multiplying 562.5 with 3 :
[tex]\longmapsto \:r {}^{3} = \frac{1687.5}{4} [/tex]
Step 4 : Dividing 1687.5 by 4 :
[tex]\longmapsto \:r {}^{3} = 421.875[/tex]
Step 5 : Finding cube root of 421.875
[tex]\longmapsto \:r = \sqrt[3]{421.875} [/tex]
Step 6 : We get :
[tex]\longmapsto \: \red{ \boxed{r = 7.5}}[/tex]
Therefore , radius of sphere is 7.5 inches .#Keep LearningPlease help me understand the question
Answer:
180 units^2
Step-by-step explanation:
The formula to find the area of a sphere is:
A=4(pi)(r)^2
A sphere with radius 2r has an area = 4π(2r)² = 4π.4r² = 16πr²
The ratio of the larger sphere to the smaller = 16πr² : 4πr² = 4 : 1
If the area of the smaller sphere is 45 units then the area of the larger sphere is 45 x 4 = 180 units^2.
hope this helps :)
{96/[36/3-(18 x 2 - 30)]} / (31-16+1)
Answer:
-1/2
Step-by-step explanation:
pemdas rules
1. 18 x 2 - 30 = 6
2. 3-6= -3
3. 36/-3 = -12
4. 96/-12 = -8
5. (31-16+1) = 16
6. -8/16 = -1/2
Multiply This Equation & Simplify:
Question Is In The Photo...
Answer:
= 12 x^8
Step-by-step explanation:
Please help. I cant figure it out
y-3x=0
2y+5x=11
solve
with elimination and substitution method
Answer:
x=1, y=3
Step-by-step explanation:
using sublimation method
y-3x=0 ....eqn(1)
2y+5x=11....eqn(2)
from eqn 1
y-3x=0
y=3x
substitute y=3x into eqn 2
2y+5x=11
2(3x)+5x=11
6x+5x=11
11x=11 (divide both sides by the coefficient of x)
x=1
since x=1 , substitute x=1 into eqn 1 to get y
y-3x=0
y-3(1)=0
y-3=0
y=3
Using elimination method
y-3x=0....eqn (1)
2y+5x=11....eqn (2)
multiply eqn 1 through by 2 and eqn 2 through by 1 to eliminate y
2y-6x=0.... eqn 3
2y+5x=11.... eqn 4
subtract eqn 4 from from eqn 3
-11x=-11 (divide both sides by the coefficient of x)
x=1
substitute x=1 into eqn 2 to get y
2y+5x=11
2y+ 5(1) =11
2y+5=11
2y=11-5
2y= 6 (divide both sides by the coefficient of y)
y=3
What integer best represents
a withdrawal of $85?
Answer:
the answer is -85 good luck on your test or honework :)
what is the perimeter of a rectangular playground 30 m long and 24 m wide
Answer:
108m
Step-by-step explanation:
2 sides are 30m long and 2 sides are 24m long.
Add all 4 sides of the playground to find the perimeter.
30m + 24m + 30m + 24m = 108 m
which of the following is an algebraic equation. a. 10+5=15. b. 10x+5=15. c. 10x+5. d. 10+5
Evaluate tan (x + pi/2) for x = pi/2
Answer:
0
Step-by-step explanation:
tan(x + [tex]\frac{\pi }{2}[/tex] ) ← substitute x = [tex]\frac{\pi }{2}[/tex]
tan([tex]\frac{\pi }{2}[/tex] + [tex]\frac{\pi }{2}[/tex] )
= tanπ
= 0
SAT scores are used by colleges and universities to evaluate undergraduate applicants. The test
scores are normally distributed. A random sample of 65 student scores has a mean of 1489 and
standard deviation of 306.
Find the 95% confidence interval for the population mean based on this sample and round to
two decimal places.
Using the t-distribution, it is found that the 95% confidence interval for the population mean is (1413.18, 1564.82).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 65 - 1 = 64 df, is t = 1.9977.
The parameters of the interval are given as follows:
[tex]\overline{x} = 1489, s = 306, n = 65[/tex].
Hence, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 1489 - 1.9977\frac{306}{\sqrt{65}} = 1413.18[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 1489 + 1.9977\frac{306}{\sqrt{65}} = 1564.82[/tex]
The 95% confidence interval for the population mean is (1413.18, 1564.82).
More can be learned about the t-distribution at https://brainly.com/question/16162795
find the average rate of change of f(x) = 3x - 7 over the interval 1 ≤ x ≤ 5
Answer:
If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.
Step-by-step explanation:
If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.
What is the circumference of a circle with a radius of 8?
Use 3.14 for pi.
Also, can someone tell me what the pattern is, here? I need to know, I can never understand.
Answer:
Step-by-step explanation:
C≈50.27
r Radius
Solution
C=2πr=2·π·8≈50.26548
The measure of one acute angle in this right triangle is 28°.
What is the measure of the other acute angle?
A. 22°
B. 28°
C. 32°
D. 62°
Answer:
[D] 62°
Step-by-step explanation:
A right triangle = 90 degree angle
A triangle = 180 degrees
Therefore,
90 + 28 = 118
180 - 118 = 62
Hence, the measure of the other acute angle is 62
Thus, the answer is [D] 62 degree
Kavinsky
Answer:
D. 62
Step-by-step explanation:
i need some urgent help
the thing is to factor the expressions trinomial way
if you want extra points you could help me with my past 2 questions they are 50 each someone gave me a wrong answer so i would really appreciate some help with that too but that's optional
#1
15x²+4x-415x²+10x-6x-45x(3x+2)-2(3x+2)(5x-2)(3x+2)#2
16a²-50a+362(8a²-25a+18)2(8a-9)(a-2)#3
63n²+126n+483(21n²+42n+16)Not more factorable
please answer the question pls
Find the sticker price and the dealer's cost for the Bobcat SX with a base price of $13,568.00. Options include air conditioning for $765.00, turbo for $643.00, towing package for $236.00, and custom wheels for $422.00. Destination charges total $365.00. The dealer pays 90% of the base price and 65% of the options.
Which choice is equivalent to the expression below?
√-125
A. 5i√5
B. -5i
C. 5i√-5
D. 5i
E. √125
Answer:
5i√5
Step-by-step explanation:
Remark
125 factors
It is factored into 5*5*5
The rule for √5*5*5 is that two can be taken outside the square root sign. I is placed in front of the root sign like 5√ and the other 5 is thrown away.
The remaining 5 is left under the root sign
As usual
√-1 is i is taken outside the root sign
Solution
5i √5 is what you get.
Least to greatest questions 7 and 8
Answer:
7.
4.7 * 10^14 , 9.99 * 10^14 , 2.9 * 10^15 , 4.5 * 10^15
8.
9.99 * 10^-8 , 4.8 * 10^-8 , 9.99 * 10^-4 , 6.5 * 10^-4
Find the sum of the first 150 positive even integers.
Answer:
Sum of first 150 positive even integers is 22650Step-by-step explanation:
We know that first 150 postive even Integers are 2,4,6,8,10... 300.
Here,
First term (a) = 2 Comman difference (d) = 4 - 2 = 2 Total terms (n) = 150Last term (aₙ) = 300[tex]\\[/tex]
Substituting values in the formula:
[tex] \\ :\implies \sf \: \: S_{n} = \dfrac{n}{2} (a + a_{n}) \\ \\[/tex]
[tex] :\implies \sf \: \: S_{n} = \dfrac{150}{2} (2 + 300) \\ \\ [/tex]
[tex] :\implies \sf \: \: S_{n} = 75(302) \\ \\ [/tex]
[tex] :\implies \: \:{ \underline{ \boxed{ \pmb{ \pink { \rm{S_{n} = 22650 }}}}}} \\ \\[/tex]
Sum of first 150 positive even integers is 22650Answer:
The number series 2, 4, 6 , 8. . . . , 150.The first term (a) = 1The common difference (d) = 4 – 2 = 2Total number of terms (n) = 150last term (an) = 300Formula for finding sum of nth terms =
n/2 × (a + an)
putting the known values ,
Sum = 150/2 × ( 2+300)
Sum = 75 × 302
Sum of first 150 positive even integers = 22650
Given the functions:
f (x) = -6x - 19
g(x) = -11x + 9
h (x) = 17x +4
Find f (3)
Answer:
f(3) = -37
Step-by-step explanation:
f (x) = -6x - 19
Let x = 3
f (3) = -6*3 - 19
= -18-19
= -37
Зу - 10 < 11
How to solve
Answer:
y<7
Step-by-step explanation:
3y-10 < 11 add 10 to both sides of the equation
3y < 21 divide by 3
y < 7
In 2018, RAND Corporation researchers found that 71% of all individuals ages 66 to 69 are adequately prepared financially for retirement. Many financial planners have expressed concern that a smaller percentage of those in this age group who did not complete high school are adequately prepared financially for retirement.
In a random sample of 300 people from the 66-69 age group who did not complete high school, 165 were not prepared financially for retirement. What is the p-value for your hypothesis test (to 4 decimals)? If your answer is zero, enter "0".
Using the z-distribution, as we are working with a proportion, it is found that the p-value of the test is of 0.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is of 71%, that is:
[tex]H_0: p = 0.71[/tex]
At the alternative hypothesis, it is tested if the proportion has decreased, that is:
[tex]H_1: p < 0.71[/tex].
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, we have that the parameters are:
[tex]n = 300, \overline{p} = \frac{165}{300} = 0.55[/tex]
Hence, the value of the test statistic is found as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.55 - 0.71}{\sqrt{\frac{0.71(0.29)}{300}}}[/tex]
z = -6.11
What is the p-value of the test?Using a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, and z = -6.11, it is found that the p-value is of 0.
More can be learned about the z-distribution at https://brainly.com/question/26454209
Mr. Smith has 847 gallons of paint. If he uses 1/3 of his paint to paint his fence, how much paint did use to paint his fence?
Answer:
282.3 gallons
Step-by-step explanation:
if needed you can round to 282
Help! please last question
Step-by-step explanation:
The centroid O cuts every median in the ratio 2:1. The distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side.
Therefore: |OD| = 2|OCI
3x-2=2(5x)
3x-2=10x
7x=-2
x=(-2/7)
Find the product of the following by writing one of numbers as the sum or difference of two numbers -
785*105
1006*95
3096*91
Answer:
Step-by-step explanation:
Use distributive property: a*(b+c) =a*b +a*c
1) 785 * 105 = 785 * (100 + 5)
= 785*100 + 785*5
= 78500 + 3925
= 82425
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2) 1006 * 95 = (1000 + 6) *95
= 1000*95 + 6*95
= 95000 + 570
= 95570
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3) 3096*91 = 3096 * (100 - 9)
= 3096*100 - 3096*9
= 309600 - 27864
= 281736