In a normal distribution, 99.7% of the data falls within three standard deviations from the mean. Given the mean of 68 and standard deviation of 4, 99.7% of the heights would range from 56 to 80 inches. Therefore, the answer is option A.
Explanation:The question is about the normal distribution, a key concept in statistics. In a normal distribution, about 68% of the values fall within one standard deviation around the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations. Since the mean height of the population is 68 inches and the standard deviation is 4 inches, three standard deviations from the mean would be 12 inches above and below the mean. Hence, 99.7% of the population's height would fall within the range of 68 inches - 12 = 56 inches and 68 inches + 12 = 80 inches.
So, the correct answer to this question is option A: 56 inches to 80 inches.
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The range within which 99.7% of the population will have a height can be found using z-scores. The correct answer is option A. 56 inches to 80 inches
Explanation:To find the range within which 99.7% of the population will have a height, we need to use the concept of z-scores.
The range is usually defined as the mean plus or minus a certain number of standard deviations.
In this case, 99.7% of the population would fall within three standard deviations of the mean.
So, the range would be 68 - (3 * 4) = 56 inches to 68 + (3 * 4) = 80 inches.
Therefore, the correct answer is A. 56 inches to 80 inches.
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Can someone help me with this
Answer:
No, because they look like they are different sizes. Or you could say the first answer
Hello There!
The answer is "C"
In this problem, you need dilation to map onto each-other.
Dilation is transformation hat changes the size of something
There are 19 sticks of gum left in one packet, and 6 sticks of gum in another packet that are going to be split evenly between 2 people. How many sticks of gum does each person get? Choose the correct answer from the choices below.
[tex]19 + 6 = 25 \div 2 = 12.5[/tex]
Answer:
12.5
Step-by-step explanation:
19+6=25 , 25÷2= 12.5
Factor this polynomial completely.
12x^2+ x-6
Answer:
(3 x - 2) (4 x + 3)
Step-by-step explanation:
Factor the following:
12 x^2 + x - 6
Factor the quadratic 12 x^2 + x - 6.
The coefficient of x^2 is 12 and the constant term is -6.
The product of 12 and -6 is -72. The factors of -72 which sum to 1 are -8 and 9.
So 12 x^2 + x - 6 = 12 x^2 + 9 x - 8 x - 6 = 3 (3 x - 2) + 4 x (3 x - 2):
3 (3 x - 2) + 4 x (3 x - 2)
Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2):
Answer: (3 x - 2) (4 x + 3)
The answer is (3 x - 2) (4 x + 3).
Polynomials
Polynomial exists an algebraic expression with terms divided utilizing the operators "+" and "-" in which the exponents of variables exist always nonnegative integers.
Factor the following:
[tex]$$12x^{2}+x-6$$[/tex]
Factor the quadratic
[tex]$12x^{2} +x-6$[/tex]
The coefficient [tex]x^{2}[/tex] is 12 and the constant term is -6.
The product of 12 and -6 is -72.
The factors of -72 which sum to 1 exist at -8 and 9.
So
[tex]$12 x^{2} +x-6=12 x^{2} +9 x-8 x-6[/tex]
[tex]=3(3 x-2)+4 x(3 x-2)$[/tex]
[tex]$3(3 x-2)+4 x(3 x-2)$[/tex]
Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2)
Hence, The answer is (3 x - 2) (4 x + 3).
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given sin28.4=.4756, cos28.4=.8796, and tan28.4=.5407 find the cot of 61.6
Answer:
The cotangent of 61.6° is .5407.
Step-by-step explanation:
Refer to the sketch attached.
61.6° + 28.4° = 90°. In other words, 61.6° is the complementary angle of 28.4°.
Consider a right triangle OAB with a 61.6° angle [tex]\rm O\hat{A}B[/tex]. The other acute angle [tex]\rm O\hat{B}A[/tex] will be 28.4°.
[tex]\displaystyle \tan{61.6\textdegree{}}=\tan{\rm O\hat{A}B} = \frac{\text{Opposite of }\rm O\hat{A}B}{\text{Adjacent of }\rm O\hat{A}B} = \frac{a}{b}[/tex].
The cotangent of an angle is the reciprocal of its tangent.
[tex]\displaystyle \cot{61.6^{\circ}}=\frac{1}{\tan{\rm O\hat{B}A}} = \frac{\text{Adjacent of }\rm O\hat{B}A}{\text{Opposite of }\rm O\hat{B}A} = \frac{a}{b} = \tan{\rm O\hat{A}B} = \tan{28.4^{\circ}}[/tex].
In other words,
[tex]\cot{61.6^{\circ}} = \tan{28.4^{\circ}} \approx 0.5407[/tex].
25 Points ! Write a paragraph proof.
Given: ∠T and ∠V are right angles.
Prove: ∆TUW ∆VWU
Answer:
Δ TUW ≅ ΔVWU ⇒ by AAS case
Step-by-step explanation:
* Lets revise the cases of congruent for triangles
- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and
including angle in the 2nd Δ
- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ
≅ 2 angles and the side whose joining them in the 2nd Δ
- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles
and one side in the 2ndΔ
- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse
leg of the 2nd right angle Δ
* Lets solve the problem
- There are two triangles TUW and VWU
- ∠T and ∠V are right angles
- LINE TW is parallel to line VU
∵ TW // VU and UW is a transversal
∴ m∠VUW = m∠TWU ⇒ alternate angles (Z shape)
- Now we have in the two triangles two pairs of angle equal each
other and one common side, so we can use the case AAS
- In Δ TUW and ΔVWU
∵ m∠T = m∠V ⇒ given (right angles)
∵ m∠TWU = m∠VUW ⇒ proved
∵ UW = WU ⇒ (common side in the 2 Δ)
∴ Δ TUW ≅ ΔVWU ⇒ by AAS case
Answer:
Step-by-step explanation:
Given ∠T and ∠V are right angles.
TW ║ UV
To prove ⇒ ΔTUW ≅ ΔVWU
Proof ⇒ In ΔTUW and ΔVUW,
∠T ≅ ∠ V ≅ 90° (given)
Side UW ≅ UW ( Common in both the triangles )
TW ║ UV
and UW is a transverse.
So ∠TWU ≅ ∠WUV [alternate interior angles]
Since Angle = Angle = side are equal
Therefore, ΔTUW ≅ ΔVWU
Jorge wants to determine the enlarged dimensions of a digital photo to be used as wallpaper on his computer screen. The original photo was 800 pixels wide by 600 pixels high. The new photo will be 1,260 pixels wide. What will the new height be?
Answer: [tex]945\ pixels[/tex]
Step-by-step explanation:
We know that the original photo was 800 pixels wide and the new photo will be 1,260 pixels wide. Therefore, we can find the scale factor.
Divide the width of the new photo by the width of the original photo. Then the scale factor is:
[tex]scale\ factor=\frac{1,260\ pixels}{800\ pixels}\\\\scale\ factor=\frac{63}{40}[/tex]
The final step is to multiply the height of the original photo by the scale factor calculated.
Therefore the height of the new photo will be:
[tex]h_{new}=(600\ pixels)(\frac{63}{40})\\\\h_{new}=945\ pixels[/tex]
Answer:
945 pixels.Step-by-step explanation:
Givens
The original photo dimensions are (800 wide x 600 high )pixelsThe new photo is 1,260 pixels wide.First, we need to find the scale factor by dividing
[tex]s=\frac{1260}{800}=1.575[/tex]
Then, we multiply the height by the scale factor
[tex]600 \times 1.575 = 945[/tex]
Therefore, the new height is 945 pixels.
Please explain now thanks
Answer:
24x - 20
Step-by-step explanation:
4(6x-5)
= 4(6x) - 4(5).............. (Distributive property)
= 24x - 20 (Ans)
Hello There!
The answer would be (24x-20)
We use order of operations so first we would multiply 4 by 6 and get 24x
then, we would multiply 4 by -5 and get -20
Your answer would be 24x - 20
NEED HELP ASAP 10 POINT QUESTION
Answer:
The original price of the car can be written in percentage which is 100%. Because the price increased by 6%, therefore, the new price should be represented as:
100% + 6% = 106% = 1.06 (remember: not 0.06, that is how much the price increased, not 0.94 either, because the price increased, not decreased).
So the answer for the first question should be:
(a) new price = 1.06 × original price
from that, we can appy the answer above for the second question:
(b) new price: $33390
Factor the trinomial below. x^2-3x-40
Answer:
(x-8) (x+5)
Step-by-step explanation:
x^2-3x-40
What 2 numbers multiply to -40 and add to -3
-8 *5 = -40
-8+5 = -3
(x-8) (x+5)
What is the value of x?
Answer:
x = 2
Step-by-step explanation:
Given 2 secants intersecting a circle from an external point, then
The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is
(x + 1)(x + 1 + 11) = (x + 4)(x + 4 + 1)
(x + 1)(x + 12) = (x + 4)(x + 5) ← expand both sides
x² + 13x + 12 = x² + 9x + 20
Subtract x² + 9x from both sides
4x + 12 = 20 ( subtract 12 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2
Polygon ABCD is translated to create polygon A’B’C’D’. Point A is located at (1,5), and point A’ is located at (-2,1). What is the distance from B to B’?
Answer:
The distance from B to B’ is [tex]5\ units[/tex]
Step-by-step explanation:
we know that
In a translation the shape and dimensions of the figure are not going to change.
therefore
AA'=BB'=CC'=DD'
Find the distance AA'
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(1,5)\\A'(-2.1)[/tex]
substitute the values
[tex]AA'=\sqrt{(1-5)^{2}+(-2-1)^{2}}[/tex]
[tex]AA'=\sqrt{(-4)^{2}+(-3)^{2}}[/tex]
[tex]AA'=\sqrt{25}[/tex]
[tex]AA'=5\ units[/tex]
therefore
[tex]BB'=5\ units[/tex]
Use the properties of exponents to rewrite the expression
(-5uv)(-5uv)(-5uv)(-5uv)
[tex]\bf (-5u)(-5u)(-5u)(-5u)\implies (-5u)^1(-5u)^1(-5u)^1(-5u)^1 \\\\\\ (-5u)^{1+1+1+1}\implies (-5u)^4\implies (-5)^4u^4\implies 625u^4[/tex]
what is the measure or angle C?
•25 degrees
•30 degrees
•60 degrees
•75 degrees
Answer:
25
Step-by-step explanation:
look B=C
so,
A+B+C=180 Sum of all <s of Tri
x+5+3x+3x=180
7x=175
x=175÷7
x=25
Answer: A or 25
Step-by-step explanation:
did the exam on edge 2020
Maria practices the piano 5/6 of an hour every day how many hours does she practice in 4 days
Answer:
20/6 or 3.33 or 3 1/3 or 3 hours and 20 mins
Step-by-step explanation:
5/6 * 4 = (5*4)/6 = 20/6
Answer:
she will have praticed 3 hours and 20 min
Step-by-step explanation:
Which of the following is the ratio between the number of successes and the number of possible outcomes of an event?
Find the value of z.
Answer:
[tex]\large\boxed{\dfrac{50}{3}}[/tex]
Step-by-step explanation:
If the polygons are similar, then the corresponding sides are in proportion:
[tex]\dfrac{z}{10}=\dfrac{20}{12}[/tex] cross multiply
[tex]12z=(10)(20)[/tex]
[tex]12z=200[/tex] divide both sides by 12
[tex]z=\dfrac{200}{12}\\\\z=\dfrac{200:4}{12:4}\\\\z=\dfrac{50}{3}[/tex]
Find the 11th term of this sequence -10, 20, -40
Answer:
Step-by-step explanation:
the nth term of the geometric sequence is : An =A1 × r^(n-1)
A1 = -10
r= -40/20=20/-10=-2
n =11
A11 = -10× (-2)^(11-1)
A11 = -10× (-2)^(10)
A11 = - 10240
Answer:
-10,240.
Step-by-step explanation:
This is a geometric sequence with common ratio 20/-10 = -40/20 = -2.
The nth term = a1r^(n-1) where a1 = the first term and r = the common ratio, so the 11th term = -10 * (-2)^ (11-1)
= -10 * 1024
= -10,240.
Find the surface area of a cylinder with a radius 19.3 ft and height 14.7 ft use a calcutor round to the nearest tenth
What are the roots of the polynomial ?
Answer:
B and E
Step-by-step explanation:
By looking at the discriminant, which is [tex]b^2-4ac[/tex], you get that [tex]5^2-4*1*7=25-28=-3[/tex]. Therefore, the only two answers with a -3 inside the square root are B and E.
Answer:
B & E
Step-by-step explanation:
see attached
Which point lies on a sphere?
J
B
S
Answer:
Point B lies on a sphere.Step-by-step explanation:
Remember, a sphere is defined as a three-dimensional object where all points on its surface are equidistant form its center.
According to its definition, all point on the boundaries can be called a point on the sphere.
So, among the options, only point B is on the sphere, because J and S are inside.
Therefore, the right answer is Point B.
A line goes through the points
(−5,−8)
and
(5,2)
. Find its slope.
Answer:
Slope is 1
Step-by-step explanation:
Rise over Run. Delta y over Delta x. -8-2/-5-5 = -10/-10 = 1
Which linear function represents the line given by the point-slope equation y – 8 = (x – 4)?
f(x) = x + 4
f(x) = x + 6
f(x) = x – 10
f(x) = x – 1
Answer:
[tex]\large\boxed{f(x)=x+4}[/tex]
Step-by-step explanation:
[tex]y-8=(x-4)\\\\y-8=x-4\qquad\text{add 8 to both sides}\\\\y-8+8=x-4+8\\\\y=x+4\to f(x)=x+4[/tex]
The equation below describes a circle. What are the coordinates of the center of the circle? (X-6)^2+(y+5)^2=15^2
Answer:
Step-by-step explanation:
6,-5 ON APEXXXXX
Answer: (6, -5)
Step-by-step explanation:
The general equation of a circle is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is center and r is radius of the circle.
Given : The equation of a circle : [tex](x-6)^2+(y+5)^2=15^2[/tex]
[tex]\Rightarrow\ (x-6)^2+(y-(-5))^2=15^2[/tex]
Comparing to the general equation of circle , we get
[tex](h,k)=(6, -5)[/tex]
Hence, the coordinates of the center of the circle = (6, -5)
cube root of y equals 4
Answer:
y = 64Step-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\sqrt[3]{y}=4\qquad\text{cube of both sides}\\\\(\sqrt[3]{y})^3=4^3\\\\y=64\\\\\bold{METHOD\ 2:}\\\\\text{Use the de}\text{finition of cube root}:\\\\\sqrt[3]{a}=b\iff b^3=a\\\\\sqrt[3]{y}=4\iff 4^3=y\to y=64[/tex]
Which mapping represent a relation is a function PLEASE HELP ASAP
Mapping A shows x--->y. A is the answer. Exactly one x value is matched to exactly one y value.
What is the radius of a circle whose equation is X^2 plus Y^2 -10X +6 X +18=0?
ANSWER
The radius is 4
EXPLANATION
The given equation is:
[tex] {x}^{2} + {y}^{2} - 10y + 6x + 18 = 0[/tex]
We complete the square to get the expression in standard form:
[tex]{x}^{2} + 6x + {y}^{2} - 10y + 18 = 0[/tex]
[tex]{x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25[/tex]
We factor using perfect squares to get:
[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = 16[/tex]
This implies that,
[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2} [/tex]
Comparing to
[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
The radius is r=4
Find the radius of a circle with the given circumference.
12 x
in.
=
6 inches
6pi
inches
12 inches
24 pi inches
Answer:
12x=2pi*r
Step-by-step explanation:
2*22/7*r=12x
r=12x*7/44
r=21x/11
The radius of a circle is calculated by dividing the given circumference by 2π. When given circumferences of 6 inches, 6π inches, 12 inches, and 24π inches, the corresponding radii are approximately 0.955 inches, 3 inches, 1.91 inches, and 12 inches, respectively.
To find the radius of a circle given its circumference, we use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Since we are given the circumference, we can rearrange this formula to solve for the radius as follows: r = C / (2π).
Given the possible circumferences provided, we can calculate the radius for each.
For 6 inches: r = 6 / (2π) = 6 / (2 * 3.14) = 6 / 6.28 = approximately 0.955 inches
For 6π inches: r = 6π / (2π) = 6 / 2 = 3 inches
For 12 inches: r = 12 / (2π) = 12 / (2 * 3.14) = 12 / 6.28 = approximately 1.91 inches
For 24π inches: r = 24π / (2π) = 24 / 2 = 12 inches
Which expression best estimates 6 3/4 divided by 1 1/2?
Answer:
7/2
Step-by-step explanation:
Round 6 3/4 to 7
Round 1 1/2 to 2
7 divided by 2
=7/2
Find the value of x in each of the following exercises:
Check the picture below.
let's notice those two corresponding angles of 90° - 2x, and also recall that the sum of all interior angles in a triangle is 180°.
[tex]\bf 60+3x+(90-2x)=180\implies x+150=180\implies x=30[/tex]
Solve the given inequality. If necessary, round to four decimal places.
13^4a < 19
Answer:
The solution of the inequality is a < 0.2870
Step-by-step explanation:
* Lets talk about the exponential function
- the exponential function is f(x) = ab^x , where b is a constant and x
is a variable
- To solve this equation use ㏒ or ㏑
- The important rule ㏒(a^n) = n ㏒(a) OR ㏑(a^n) = n ㏑(a)
* Lets solve the problem
∵ 13^4a < 19
- To solve this inequality insert ㏑ in both sides of inequality
∴ ㏑(13^4a) < ㏑(19)
∵ ㏑(a^n) = n ㏑(a)
∴ 4a ㏑(13) < ㏑(19)
- Divide both sides by ㏑(13)
∴ 4a < ㏑(19)/㏑(13)
- To find the value of a divide both sides by 4
∴ a < [㏑(19)/㏑(13)] ÷ 4
∴ a < 0.2870
* The solution of the inequality is a < 0.2870
Answer:
a < 0.2870
Step-by-step explanation:
We are given the following inequality which we are to solve, rounding it to four decimal places:
[tex] 1 3 ^ { 4 a } < 1 9 [/tex]
To solve this, we will apply the following exponent rule:
[tex] a = b ^ { l o g _ b ( a ) } [/tex]
[tex]19=13^{log_{13}(19)}[/tex]
Changing it back to an inequality:
[tex]13^{4a}<13^{log_{13}(19)}[/tex]
If [tex]a > 1[/tex] then [tex]a^{f(x)}<a^{g(x)}[/tex] is equivalent to [tex]f(x)}< g(x)[/tex].
Here, [tex]a=13[/tex], [tex]f(x)=4a[/tex] and [tex]g(x)= log_{13}(19)[/tex].
[tex]4a<log_{13}(19)[/tex]
[tex]a<\frac{log_{13}(19)}{4}[/tex]
a < 0.2870