Answer:
[tex]\frac{6}{40}=\frac{3}{20}[/tex]
Step-by-step explanation:
The experimental probability is the number of times the desired result was obtained over the total number of times the experiment was carried out:
[tex]P=\frac{TimesTheEventOccurs}{TotalNumberOfTrials}[/tex]
In this case the Event we are looking for is rolling a 3 on the number cube.
The total number of trials is:
40
because the student rolls the cube 40 times.
and the times that he got the number 3 (the times the desired event occurs) is:
6
because he rolls a 3 on the number cube 6 times.
Thus our experimental probability to roll a 3 is:
[tex]P=\frac{6}{40}[/tex]
Marcia's wages are £260 per week.
She wants to save some money to buy a computer.
The computer costs £218.
Marcia is going to save 5% of her wages each week.
How many weeks will it take her to save enough money to buy the computer?
Answer:
17 weeks
Step-by-step explanation:
Please refer to the picture attached.
At the end of each week, she will be able to save 13 dollars. I'm the 17th week, whe will save more than 218 dollars and will be able to afford to buy the computer.
However, in 16th week, she will only save 208 dollars which is insufficient to buy the laptop.
Hence, u round up the value of x in order to get the answer.
If x^6=60 and w^10=20, what is x^12×w^-10? A. 36, B. 60, C. 180 or D. 360
Answer:
[tex] x^{12} w^{-10}[/tex]
And we can find this rewriting the expression in terms of the info given and we got:
[tex]x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}[/tex]
And replacing we got:
[tex]x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180[/tex]
And the best option would be:
C. 180
Step-by-step explanation:
For this case we know that:
[tex] x^6, w^{10} = 20[/tex]
And we want to find the value for:
[tex] x^{12} w^{-10}[/tex]
And we can find this rewriting the expression in terms of the info given and we got:
[tex]x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}[/tex]
And replacing we got:
[tex]x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180[/tex]
And the best option would be:
C. 180
The National Cancer Institute estimates that 3.65% of women in their 60s get breast cancer. A mammogram can typically identify correctly 85% of cancer cases and 95% of cases without cancer. What is the probability that a woman in her 60s who has a positive test actually has breast cancer?
Answer:
39.17% probability that a woman in her 60s who has a positive test actually has breast cancer
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Positive test.
Event B: Having breast cancer.
3.65% of women in their 60s get breast cancer
This means that [tex]P(B) = 0.0365[/tex]
A mammogram can typically identify correctly 85% of cancer cases
This means that [tex]P(A|B) = 0.85[/tex]
Probability of a positive test.
85% of 3.65% and 100-95 = 5% of 100-3.65 = 96.35%. So
[tex]P(A) = 0.85*0.0365 + 0.05*0.9635 = 0.0792[/tex]
What is the probability that a woman in her 60s who has a positive test actually has breast cancer?
[tex]P(B|A) = \frac{0.0365*0.85}{0.0792} = 0.3917[/tex]
39.17% probability that a woman in her 60s who has a positive test actually has breast cancer
What’s the correct answer for this?
Answer:
Tangent
Step-by-step explanation:
Tangent intersects a circle at exactly one point
Simplify the following expression.
(2x + 5) + (3x2 + 7x + 3)
Answer:
3x^2 + 9x + 8
Step-by-step explanation:
2x+5+3x^2+7x+3
2x+5+3x^2+7x+3
(3x^2)+(2x+7x)+ (5+3)
3x^2+9x+8
2. Find the measure of angle G. Round your answer to the nearest degree.
Answer:
G = 53 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin G = 24/30
Take the inverse sin of each side
sin ^-1 sin G = sin ^-1 (24/30)
G =53.13010235
To the nearest degree
G = 53 degrees
Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is gbb, then R9gbb)=1. Suppose that the random variable X is defined in terms of R as follows: X=2R^2-4R-2. The values of X are thus:
Complete Question
The complete question is shown on the first uploaded image
Answer:
Value x of X -3 -7 -15
[tex]P_X (x)[/tex] [tex]\frac{1}{2}[/tex] [tex]\frac{3}{8}[/tex] [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
From the question we are told that
The values of X are [tex]X = -3 , -7 , -15[/tex]
The total number of outcomes is n = 8
The probability distribution function of X is evaluated as follow
[tex]p(X = -3 ) = \frac{N_{-3}}{n}[/tex]
Where [tex]N{-3}[/tex] is the number of time X = -3 occurred and from the table the value is [tex]N _{-3} = 4[/tex]
Therefore
[tex]p(X = -3 ) = \frac{4}{8}[/tex]
[tex]p(X = -3 ) = \frac{1}{2}[/tex]
Now
[tex]p(X = -7 ) = \frac{N_{-7}}{n}[/tex]
Where [tex]N_{-7} = 3[/tex] from table
So
[tex]p(X = -7 ) = \frac{3}{8}[/tex]
Also
[tex]p(X = -15 ) = \frac{N_{-15}}{n}[/tex]
[tex]p(X = -15 ) = \frac{1}{8}[/tex]
You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37. A random sample of 780 men over the age of 50 found that 206 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim. Test the relevant hypotheses using a 10% level of significance. Give answers to at least 4 decimal places. What are the correct hypotheses?
Answer:
1. Yes, the sample data provides convincing evidence to support the claim that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37
2. The correct hypotheses are;
The null hypothesis is H₀: p ≥ p₀
The alternative hypothesis is Hₐ: p < p₀
Step-by-step explanation:
given
The null hypothesis is H₀: p ≥ p₀ where p₀ = 0.37
The alternative hypothesis is Hₐ: p < p₀
The formula for the z test is presented as follows;
[tex]z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0 (1 - p_0)}{n}}}[/tex]
Where:
[tex]\hat p[/tex] = Sample proportion = 206/780 = 0.264
p₀ = Population proportion = 0.37
n = Sample size = 780
α = Significance level = 10% = 0.01
Plugging in the values, we have;
[tex]z=\dfrac{0.264-0.37}{\sqrt{\dfrac{0.37 (1 - 0.37)}{780}}} = -6.13[/tex]
From the the z relation/computation, we have the p value = 0.000000000451
Since the p value which is 0.000000000451 is less than α, which is 0.01 we reject the null hypothesis and we fail to reject the alternative hypothesis, that is there is sufficient statistical evidence to suggest that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37.
This question is rlly confusing
Answer: C.
Step-by-step explanation:
To find the discounted value off of a full price, you can multiply the full price by the discount percentage to find the discount:
250 * 0.20 = 50
The discount is 50 dollars.
The laptop costs $250, but with the discount of $50, it is now for sale for $200.
The correct answer is C.
how and explain how to find the value of x . step by step I will give the most correct one the brainiest
Answer:
X=96
Step-by-step explanation:
180-134=46
180-130=50
SUM OF TWO INTERIOR ANGLES = EXTERIOR ANGLE
50 + 46=96
What is the center of the circle and the radius
X2+y2-4x+12y-24=0
Answer:
Subtract
31
31
from both sides of the equation.
x
2
+
y
2
−
4
x
−
12
y
=
−
31
x2+y2-4x-12y=-31
Complete the square for
x
2
−
4
x
x2-4x
.
Tap for more steps...
(
x
−
2
)
2
−
4
(x-2)2-4
Substitute
(
x
−
2
)
2
−
4
(x-2)2-4
for
x
2
−
4
x
x2-4x
in the equation
x
2
+
y
2
−
4
x
−
12
y
=
−
31
x2+y2-4x-12y=-31
.
(
x
−
2
)
2
−
4
+
y
2
−
12
y
=
−
31
(x-2)2-4+y2-12y=-31
Move
−
4
-4
to the right side of the equation by adding
4
4
to both sides.
(
x
−
2
)
2
+
y
2
−
12
y
=
−
31
+
4
(x-2)2+y2-12y=-31+4
Complete the square for
y
2
−
12
y
y2-12y
.
Tap for more steps...
(
y
−
6
)
2
−
36
(y-6)2-36
Substitute
(
y
−
6
)
2
−
36
(y-6)2-36
for
y
2
−
12
y
y2-12y
in the equation
x
2
+
y
2
−
4
x
−
12
y
=
−
31
x2+y2-4x-12y=-31
.
(
x
−
2
)
2
+
(
y
−
6
)
2
−
36
=
−
31
+
4
(x-2)2+(y-6)2-36=-31+4
Move
−
36
-36
to the right side of the equation by adding
36
36
to both sides.
(
x
−
2
)
2
+
(
y
−
6
)
2
=
−
31
+
4
+
36
(x-2)2+(y-6)2=-31+4+36
Simplify
−
31
+
4
+
36
-31+4+36
.
(
x
−
2
)
2
+
(
y
−
6
)
2
=
9
(x-2)2+(y-6)2=9
This is the form of a circle. Use this form to determine the center and radius of the circle.
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
(x-h)2+(y-k)2=r2
Match the values in this circle to those of the standard form. The variable
r
r
represents the radius of the circle,
h
h
represents the x-offset from the origin, and
k
k
represents the y-offset from origin.
r
=
3
r=3
h
=
2
h=2
k
=
6
k=6
The center of the circle is found at
(
h
,
k
)
(h,k)
.
Center:
(
2
,
6
)
(2,6)
These values represent the important values for graphing and analyzing a circle.
Center:
(
2
,
6
)
(2,6)
Radius:
3
3
Answer:
center: (2,-6)
radius: 8
Step-by-step explanation:
trust me i checked khan academy
During a trip, Amy had to take two different trains. Her first train traveled for 3 hours, and the second
train traveled for 4 hours. Combined, the trains traveled 625 miles.
If the equation 3m + 4n = 625 represents this situation, which statements are true regarding this
equation?
Select two that apply.
The variable m in the equation represents the speed of the first train.
The variable m in the equation represents the speed of the second train.
The variable n in the equation represents the speed of the second train.
The variable n in the equation represents the speed of the first train.
The variable m in the equation represents the number of hours Amy traveled on the
first train.
The variable n in the equation represents the number of hours Amy traveled on the
second train.
Answer:
Let's solve for m.
3m + 4n = 625
Step 1: Add -4n to both sides.
3m + 4n + −4n = 625 + −4n
3m = −4n + 625
Step 2: Divide both sides by 3.
3m/3 = 4n + 625/3
m = -4/3 n + 625/3
C) The variable m in the equation represents the number of hours Amy traveled on the
first train.
D) The variable n in the equation represents the number of hours Amy traveled on the
second train.
Consider triangle ABC. The legs have a length of 5 units each. Triangle A B C is shown. Angle A C B is a right angle. The lengths of sides A C and C B are 5. The length of the hypotenuse c is unknown. What is the length of the hypotenuse of the triangle? 5 units 5 StartRoot 2 EndRoot units 10 units 10 StartRoot 2 EndRoot units
Answer:
Hypotenuse = 5√2 units
Step-by-step explanation:
Triangle ABC:
The legs are 5 units each
Opposite = 5unit
Adjacent = 5unit
Triangle ACB:
lengths of sides A C and C B are 5
The legs are 5 units each
Leg =AC = Opposite = 5unit
Leg = CB = Adjacent = 5unit
The hypotenuse for both ∆ACB is unknown. Since ∆ACB is a right angled triangle, we would apply Pythagoras theorem to find the hypotenuse.
Using Pythagoras theorem:
Hypotenuse ² = opposite ² + adjacent ²
Hypotenuse ² = leg² + leg²
AB = hypotenuse in ∆ACB
AB² = 5² + 5²
AB² = 25+25 = 50
AB = √50 = √(25×2)
AB = 5√2
Hypotenuse = 5√2 units
Answer:
The answer is B! Person above me is right!
Step-by-step explanation:
The product of two consecutive positive integers is 132. What are the integers?
Answer:
The integers are 11 and 12
Step-by-step explanation:
11 and 12 are consecutive positive integers, and 11 x 12 = 132.
BC =
Round your answer to the nearest hundredth.
B
35°
6
А
Using the cosine ratio, the length of BC to the nearest hundredth is: 4.91.
What is the Cosine Ratio?Cosine ratio is: cos ∅ = adjacent side/hypotenuse
Given the right triangle in the diagram above, thus:
∅ = 35°Adjacent = ? = BCHypotenuse = 6Thus:
cos 35 = BC/6
BC = cos 35 × 6
BC = 4.91
Thus, using the cosine ratio, the length of BC to the nearest hundredth is: 4.91.
Learn more about cosine ratio on:
https://brainly.com/question/15793827
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
It is the complement of the circle in the square
Okay,
Let the square be Universal set(U) and the circle be A
So
A complement = A' = U-A So
The shaded area is the complement of the circle
what is the area of a circle with a diameter of 8
Step-by-step explanation:
Radius (R) =diameter /2 =8/2 =4
So area=
[tex]\pir {r}^{2} = \pi {4}^{2} = 50.27[/tex]
Hope this helps..
Nicole has x beads. Together we have 56 beads. How many beads will I have if I lose 1/4 of my beads?
Answer:
(56 - x) * 3/4
Step-by-step explanation:
x + y = 56
y = 56 - x
y' = (56 - x) * 3/4
What are the answers to a b and c ?
You've found yourself trapped in a desert, desperate for a drink of water. Amazingly, you come across a food cart right there and they have glasses of water available for just $1! You even have a dollar! You're all set. Except the cart vendor tells you He only sells 80z glasses of water, and he only have 6oz and 10oz glasses. "I'll pay a dollar for the 6oz!" you say. "No," he replies, "I won't be cheating you." How can you use the 6oz glass and the 10oz glass to measure out exactly 8oz?
If I'm understanding the problem correctly, the vendor sells water in exactly 8 oz increments, but only has glasses that can hold 6 oz or 10 oz.
Fill up the 10 oz glass, then (carefully) pour its contents into a 6 oz glass until it it is full. Then the 10 oz glass should contain 4 oz of water. Drink the 4 oz, repeat this process to get your 8 oz, and pay the man.
arc
An 8 inch pie (diameter is 8) was sliced into 4 equal parts. How large is the 2 points
pie crust of one slice? *
Answer:
6.28 inches
Step-by-step explanation:
Given that the diameter of the pie=8 inch
Radius=Diameter/2
Therefore: Radius of the pie=8/2=4 Inch
Circumference of a circle [tex]=2\pi r[/tex]
Since the pie is sliced into 4 equal parts:
Length of the Pie crust of one slice[tex]=\dfrac{2\pi r}{4}[/tex]
Substituting the value of r, we obtain:
Length of the Pie crust of one slice[tex]=\dfrac{2*\pi *4}{4}\\=2\pi $ inches\\=6.28 inches (correct to 2 decimal places)[/tex]
Bromeliads are tropical flowering plants. Many are epiphytes that attach to trees and obtain moisture and nutrients from air and rain. Their leaf bases from cups that collect water and are home to larvae of many insects. As a preliminary to study of changes in the nutrient cycle, Jacqueline Ngai and Diane Srivastava examined the effects of adding nitrogen, phosphorus, or both to the cups. They randomly assigned 8 bromeliads growing in Costa Rica to each of four treatment groups, including an unfertilized control group. A monkey destroyed one of the plants in the control group, leaving 7 bromeliads in that group. Here are the numbers of new leaves on each plant over the seven months following fertilization:
Nitrogen Phosphorus Both Neither
16 14 14 11
15 14 16 13
15 14 15 16
17 11 14 15
17 13 14 15
18 12 13 11
18 15 17 12
13 15 14
(a) Give the degrees of freedom for the F statistic.
numerator degrees of freedom
denominator degrees of freedom
(b) Find the F-statistic. (Round your answer to two decimal places.)
F =
(c) Find the associated P-value. (Round your answer to four decimal places.)
(d) State conclusions. Select the correct answer.We have significant evidence at the 5% level that the means are not all the same.We do not have significant evidence at the 5% level that the means are not all the same..
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
Y: number of new leaves of Bromeliads grown under different types of fertilization.
Factor: Type of fertilizer
Treatments: 1. Nitrogen, 2. Phosphorus, 3. Both, 4. Neither (control group)
To compare these four groups you have to conduct an ANOVA
The hypotheses are:
H₀: μ₁= μ₂= μ₃= μ₄
H₁: At least one population mean is different from the others.
α: 0.05
a)
The degrees of freedom of the F-statistic are:
[tex]F_{I-1;N-I}= F_{4-1;31-4}= F_{3;27}[/tex]
I= number of treatments
N= total number of experimental units (in all groups)
b)
SSTreatments= 39.37
SSError= 72.18
MSTreatments= SStreatments/DfTreatments= 39.37/3= 13.12
MSError=SSError/DfError= 72.18/27= 2.67
[tex]F= \frac{MS_{Treatments}}{MS_{Error}} = \frac{13.12}{2.67} = 4.91[/tex]
c)
This test is one-tailed to the right and so is the p-value:
P(F₃;₂₇≥4.91)= 1 - P(F₃;₂₇<4.91)= 1 - 0.9925= 0.0075
d)
The decision rule using the p-value is:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The p-value is less than α, the test is significant at 5% significance level.
"We have significant evidence at the 5% level that the means are not all the same."
I hope this helps!
Activity Question 1 When designing a truss, a truss builder might know the base angle measurement and the length of the tie beam needed. The next step is to compute the height of the king post. Let's take a look at some right triangles to see whether knowing the measure of an acute angle of a right triangle and the length of one of the sides is enough to find the lengths of the other two sides. Part A What is the measure of ∠BAC?
Answer:
36.87°
Step-by-step explanation:
Assume the triangles are as in the diagram below.
∠BAC includes ∠DAE.
The measure of ∠BAE is 36.87°.
Answer:
36.87°
Step-by-step explanation:
i just had this question on edmentum and it was right.
Simplify the expression
(8y^2)(-9y^2)
Answer:
-72 y^4
Step-by-step explanation:
(8y^2)(-9y^2)
Multiply the coefficients
8*-9 = -72
Add the exponents since the bases are the same
y^2 * y^2 = y^(2+2) = y^4
(8y^2)(-9y^2) = -72 y^4
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
C. [tex](f+g)(x)=-5^x-3x-6[/tex]
Step-by-step explanation:
→Set it up, like so:
[tex](-5^x-4)+(-3x-2)[/tex]
[tex]-5^x-4-3x-2[/tex]
→Add like terms (-4 and -2):
[tex]-5^x-3x-6[/tex]
The art teacher needs 70 markers for her classes. The markers come in packages of 15. How many packages of markers will the art teacher need to buy?
Answer:
5
Step-by-step explanation:
Take the number of markers and divide by the number in each package
70/15
4.6666repeating
Round to the nearest whole number to determine the number of packages
5
They will need to buy 5 packages
In circle O two secants,
ABP and CDP, are drawn to external point P. If mAC = 72°, and mBD = 34°, what is the measure of ∠P?
(1) 19° (3) 53°
(2) 38° (4) 106°
Answer:
(1)19°
Step-by-step explanation:
The diagram is drawn and attached below.
Let x=mAC = 72°; and
y=mBD = 34°
By the Angle-Arc relationship, the external angle is half the difference.
[tex]\angle P=\frac{1}{2}(x^\circ-y ^\circ)\\$Therefore:\\m\angle P=\frac{1}{2}(72^\circ-34 ^\circ)\\m\angle P=19^\circ[/tex]
Find m
A) 110
B) 222
C) 28
D) 82
Answer:
As angel WVU = angel WVF + angel FVU
Therefore angel WVF =152 - 70
so, angel WVF = 82
In a survey of first graders, their mean height was 49.9 inches with a standard deviation of 3.15 inches. Assuming the heights are normally distributed, what height represents the first quartile of these students?
Answer:
Height = 47.77 inches
Step-by-step explanation:
We are given;
Mean = 49.9 in
Standard deviation;SD = 3.15 in
The first quartile is the 25th percentile, which means it's where 25% of the data falls.
Now from the normal distribution table attached, we can see that the z-value for 25% or 0.25 is approximately
-0.675.
To find the height that represents the first quartile of these students, we will use the formula;
z = (height - mean)/(SD)
Making height the subject ;
height = (z × SD) + mean
Plugging in the relevant values to obtain;
Height = (-0.675 × 3.15) + 49.9
Height ≈ 47.77 inches
a bear travel 15km at an angle of 135 degrees from his den. it then travels for 3.7 km at an orientation of 55 degrees. the bear ends his trip walking 12 km at an orientation of 320 degrees. what distance is the bear from his den?
Answer:
30.7
Step-by-step explanation:
add the 15,3.7 ,and the 12
