Answer:
Yes to both.
Step-by-step explanation:
Similar means the same shape but the sizes may be different.
Right angles are similar and so are equilateral triangle.
Right triangles are not necessarily similar unless they have the same hypotenuse and an acute angle. All equilateral triangles are similar because they have equal angles and sides. This discussion relates to the nature of mathematical truths, which are absolute in their systems, compared to observational truths that rely on variable sensory evidence.
Not all right triangles are similar because they can have different ratios between their sides despite having a right angle. However, if two right triangles have the same length of their hypotenuse and an acute angle correspondingly, they are indeed similar according to a mathematical corollary.
In contrast, all equilateral triangles are similar because they all have equal angles (60 degrees each) and their side lengths are also in the same ratio, which is 1:1:1, making them the same shape, although they can be different sizes.
This connects to the larger questions about mathematical truths. For instance, the statement that the three interior angles of a triangle are equivalent to two right angles is a mathematical truth that is similar to definitional truths, such as 'green is a color,' since both are based on definitions and logical deductions in their respective systems.
However, mathematical truths differ from observational truths like 'there is beer in the refrigerator' because observational truths are subject to sensory evidence which can change, whereas mathematical truths are absolute within the context of their axiomatic systems.
When considering questions that lead to insights into forms, mathematical questions are often better suited over observational ones as they transcend physical reality and provoke a more abstract level of reasoning.
what is the equation of the line that passes through point (4, 12) and has a intercept of -2
Answer:
[tex]\large\boxed{y=\dfrac{7}{2}x-2}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the point (4, 12), and y-intercept b = -2 → (0, -2).
Substitute:
[tex]m=\dfrac{-2-12}{0-4}=\dfrac{-14}{-4}=\dfrac{14:2}{4:2}=\dfrac{7}{2}[/tex]
Finally:
[tex]y=\dfrac{7}{2}x-2[/tex]
Solve x2 – 8x = 3 by completing the square. Which is the solution set of the equation?
(4 minus StartRoot 19 EndRoot comma 4 + StartRoot 19 EndRoot)
(4 minus StartRoot 11 EndRoot comma 4 + StartRoot 11 EndRoot)
(4 minus StartRoot 8 EndRoot comma 4 + StartRoot 8 EndRoot)
(4 minus StartRoot 3 EndRoot comma 4 + StartRoot 3 EndRoot)
Answer:
x = 4 ± [tex]\sqrt{19}[/tex]
Step-by-step explanation:
Given
x² - 8x = 3
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = 3 + 16
(x - 4)² = 19 ( take the square root of both sides )
x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )
x = 4 ± [tex]\sqrt{19}[/tex], that is
x = 4 - [tex]\sqrt{19}[/tex], 4 + [tex]\sqrt{19}[/tex]
Final answer:
The solution set for the quadratic equation x² - 8x = 3 is found by completing the square, resulting in (4 - √19, 4 + √19).
Explanation:
To solve the quadratic equation by completing the square, we start with x² – 8x = 3. First, we move the constant term to the other side of the equation:
x² – 8x + ____ = 3 + ____
Now we need to find a number to fill in the blanks that makes the left side a perfect square trinomial. To do this, take half of the coefficient of x, which is -8/2 = -4, and then square it, which gives us 16. Add 16 to both sides:
x² – 8x + 16 = 3 + 16
x² – 8x + 16 = 19
The left side is now a perfect square, (x – 4)² = 19. Taking the square root of both sides gives us:
x – 4 = ±√19
Add 4 to both sides to solve for x:
x = 4 ±√19
Therefore, the solution set for the equation x² – 8x = 3 is (4 – √19, 4 + √19).
Divide 13 by v. Then, subtract 7.
Which of the following expressions matches the statement above?
A. 13 ÷ (v - 7)
B. 13 ÷ (7 - v)
C. 13 ÷ v - 7
D. v ÷ 13 - 7
find the values of x and y that satisfy the equation.
-10x+12i=20+3yi
Answer:
x = -2
y = 4
Step-by-step explanation:
Given
[tex]-10x+12i=20+3yi[/tex]
Two complex numbers are equal when they have equal real and imaginary parts.
Equate real parts:
[tex]-10x=20\\ \\x=-\dfrac{20}{10}=-2[/tex]
Equate imaginary parts:
[tex]12=3y\\ \\y=\dfrac{12}{3}=4[/tex]
Final answer:
The values of x and y that satisfy the given complex equation are x = -2 and y = 4, found by equating the real and imaginary parts respectively.
Explanation:
To find the values of x and y that satisfy the equation -10x + 12i = 20 + 3yi, we need to equate the real parts and the imaginary parts of the complex numbers on both sides of the equation.
For the real parts, we have:
-10x = 20
=> x = -2
For the imaginary parts, we have:
12 = 3y
=> y = 4
So the solution for the equation is x = -2 and y = 4.
what is the solution to this equation 8x-5(x-3)=18
Answer:
x=1
Step-by-step explanation:
use distributive property for the negative 5, then simplify, then bring the 15 to the other side, then divide by 3. picture included.
9. Alicia Martin's savings account has a principle of $1,200. It earns 6% interest compounded quartly
for two quarters
10. Aubrey Daniel's savings account has a principle of $5,725. It earns 4% interest compounded
quarterly for 3 years.
11. The principle of Angelo Carrera's savings account is $9,855. It earns 6% interest compounded
quarterly for 2 quarters.
12. Milo Simpson deposited $860 in a new regular savings account that's earns 5.5% interest
compounded semiannually for 1 year,
13. Jana Lacey deposits $4,860in a new credit union savings account on the first day of the quarter.
The principle earns 4% interest compounded quarterly for 6 months.
Answer:
[tex]9) \$1236.27\,10)\,\$6451.07\, 11)\,\$10,152.87 \,12)\,\$907.95 \,13)\,\$4957.69[/tex]
Step-by-step explanation:
9) Since Alicia Martin's savings earns 6% quarterly for two quarters then:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] ⇒ Amount (A), Principle (P), rate (r) in decimal form, number of compoundings (n) a year and t, in year or its fractions.
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=1200(1+\frac{0.06}{4})^{4*\frac{1}{2}}\Rightarrow A=\$1236.27[/tex]
10) Aubrey Daniel's case:
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=5725(1+\frac{0.04}{4})^{4*3}\Rightarrow A\approx \$6451.07[/tex]
11) As for Angelo, similarly to Alicia.
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=9855(1+\frac{0.06}{4})^{4*\frac{1}{2}}\Rightarrow A\approx \$10,152.87[/tex]
12) Simpson's. For semiannual n=2
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=860(1+\frac{0.055}{2})^{2*1}\Rightarrow A\approx \$907.95[/tex]
13) Jana Lacey amount:
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=4860(1+\frac{0.04}{4})^{4*\frac{1}{2}}\Rightarrow A\approx \$4957.69[/tex]
Abigail bought 15 chicken wings for $18. What was the cost of the wings in wings per dollar?
Answer:
$1.20 per chicken wing
Step-by-step explanation:
15 chicken wings = $18
1 chicken wing = $18/15 = $6/5 = $1.20
Which function has the same graph as x + y = 11? A. f(x) = -y + 11 B. f(x) = -x + 11 C. f(x) = x − 11 D. f(x) = y − 11
The real is B.) f(x) = -x + 11
A.) f(x) = -y + 11 is the wrong answer.
I have pictures to prove that they are the same in the graph as x + y = 11.
Hope this will help a lot more than the other answer.
Answer:
B.) f(x) = -x + 11
Step-by-step explanation:
Hello there. May somebody help me simplify this problem? It would be very kind.
It is about radicals etc.
Answer:
27 / (4x⁶y⁸)
Step-by-step explanation:
[tex]\frac{4(3x^{2}y^{4})^{3}}{(2x^{3}y^{5})^{4}}[/tex]
When raised to a power, multiply the exponents.
[tex]\frac{4(3^{3}x^{6}y^{12})}{2^{4}x^{12}y^{20}} \\\\\frac{2^{2}3^{3}x^{6}y^{12}}{2^{4}x^{12}y^{20}}[/tex]
When dividing, subtract the exponents.
[tex]2^{2-4}3^{3}x^{6-12}y^{12-20}\\2^{-2}3^{3}x^{-6}y^{-8}[/tex]
Move negative exponents to the denominator.
[tex]\frac{3^{3}}{2^{2}x^{6}y^{8}}\\\frac{27}{4x^{6}y^{8}}[/tex]
What is the length of segment A.B.
Answer:
The distance between A and B is l(AB) = 13 units
Step-by-step explanation:
Given:
let,
A ≡ ( x1, y1 ) ≡ ( 0, 12 )
B ≡ ( x2, y2 ) ≡ ( 5, 0 )
To Find:
Length AB = ?
Solution:
Distance Formula for the distance between the two points ( x1, y1 ) and ( x2, y2 ) we have,
[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
On substituting the above values we will get,
[tex]l(AB) = \sqrt{((5-0)^{2}+(0-12)^{2} )}\\l(AB)=\sqrt{(5^{2} +(-12)^{2} } \\l(AB)=\sqrt{(25+144)}\\ l(AB)=\sqrt{169} \\l(AB)=13\ unit[/tex]
Therefore the distance between A and B is l(AB) = 13 units
MaryAnn is printing pictures from her recent trip to Europe. An online print shop charges $0.15 per
4x6 inch print, along with a flat rate shipping charge of $3.00. If MaryAnn has $35 to spend, how
many prints can she order?
Answer:
213
Step-by-step explanation:
Let
x = number of picturesy = total priceThe relationship between x and y can be represented through a linear equation.
y = a . x + b
where,
a is the slope
b is the y-intercept
The slope refers to the price per print, that is, a = $0.15/p.
Then,
y = $0.15/p . x + b
Even if x = 0, there is a fixed cost of $3.00 (y = $3.00). We can replace these values in the expression above.
$3.00 = $0.15/p . 0 + b
b = $3.00
The final equation is:
y = $0.15/p . x + $3.00
If MaryAnn has $35,
$35 = $0.15/p . x + $3.00
$32 = $0.15/p . x
x = 213 p
She can order 213 prints.
What is y+x=5 in function notation? The dependent variable is y.
Answer:
f(x)=5-x
Step-by-step explanation:
The equation y + x = 5 in function notation is f(x) = 5 - x, done by isolating the dependent variable, y, and expressing it as a function of x.
Explanation:The equation y + x = 5 can be rewritten in function notation by isolating the dependent variable, y, which is standard procedure in function notation. To isolate y, we need to subtract x from both sides of the equation. Thus, the equation y + x = 5 becomes y = 5 - x. In function notation, where y is typically written as f(x), this would become f(x) = 5 - x.
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Find the x- and y intercepts for the linear equation
4. 3x + 2y = 6
5. 4x – 9y = 36
6. x + y = -3
8. Xx - 3y = 12
4. 3x + 2y = 6
x-intercept = 2 , y - intercept = 3
5. 4x – 9y = 36
x-intercept = 9, y - intercept = -4
6. x + y = -3
x-intercept = -3, y - intercept = -3
8. x - 3y = 12
x-intercept = 12, y - intercept = -4
Step-by-step explanation:
To find the x-intercept we put y=0 in the equation and to find the y-intercept we put x = 0 in the equation
4. 3x + 2y = 6
Putting y = 0
[tex]3x + 2y = 6\\3x +2(0) = 6\\3x = 6\\\frac{3x}{3} = \frac{6}{3}\\x= 2[/tex]
Putting x=0
[tex]3x + 2y = 6\\3(0) + 2y = 6\\2y = 6\\\frac{2y}{2} = \frac{6}{2}\\y= 3[/tex]
5. 4x – 9y = 36
Putting y = 0
[tex]4x -9y = 36\\4x - 9(0) = 36\\4x = 36\\\frac{4x}{4} = \frac{36}{4}\\x = 9[/tex]
Putting x=0
[tex]4(0) -9y = 36\\-9y=36\\\frac{-9x}{-9} = \frac{36}{-9}\\x =-4[/tex]
6. x + y = -3
Putting y = 0
[tex]x+y=-3\\x+0 = -3\\x = -3[/tex]
Putting x=0
[tex]x + y = -3\\0+y=-3\\y=-3[/tex]
8. X - 3y = 12
Putting y=0
[tex]x - 3(0) = 12\\x -0 = 12\\x = 12[/tex]
Putting x = 0
[tex]0-3y = 12\\-3y = 12\\\frac{-3y}{-3} =\frac{12}{-3}\\y=-4[/tex]
Keywords: Linear equation
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Which of the following expressions represents the statement below?
two times the sum of a number and 9
A. 9n + 2
B. 9(n + 2)
C. 2n + 9
D. 2(n + 9)
Option D. 2(n + 9) is the right answer
Step-by-step explanation:
The word problems are converted into mathematical problems to solve simply.
for the given problem
"two times the sum of a number and 9"
Let n be a number then
when there is and between two things they are performed first then next operation is performed so
the sum of a number and 9
[tex]n+9[/tex]
Then
two times the sum of a number and 9
[tex]2(n+9)[/tex]
Hence,
Option D. 2(n + 9) is the right answer
Keywords: Mathematical notation
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Final answer:
The correct expression is '2(n + 9),' which corresponds to choice D and represents two times the sum of a number and 9.
Explanation:
The expression that represents the statement 'two times the sum of a number and 9' is D. 2(n + 9). This is because you first need to find the sum of the number (let's call it n) and 9, which is represented as (n + 9). Then, the statement says 'two times' which means you need to multiply that sum by 2, resulting in 2 × (n + 9).
8 lb 1 oz − 3 lb 6 oz
Answer:
4.6875 is the answer
Step-by-step explanation:
First, lets put both into just ounces. (1lb = 16oz.)
8lb. 1oz. = 129oz.
3lb. 6oz. = 54oz.
Second, subtract.
129 - 54 = 75
Third, put into pounds and ounces.
75oz. = 4lb. 11oz.
_______
Best Regards,
Wolfyy :)
8. Find the value of k, if (1-1) is a solution of the equation 3x-ky =8. Also, find the coordinates of
another point lying on its graph.
Answer:
k = 5 and (6,2).
Step-by-step explanation:
Since (1,-1) is a solution of the equation 3x - ky = 8, so the point (1,-1) will satisfy the equation above.
Hence, putting x = 1 and y = -1 in the equation will give left-hand side = right-hand side.
So, 3(1) - k(-1) = 8
⇒ 3 + k = 8
⇒ k = 5 (Answer)
Therefore, the equation of the straight line is 3x - 5y = 8 ....... (1)
Now, putting x = 6 , then from equation (1) we get y = 2
Therefore, (6,2) is also a point on the graph of equation (1). (Answer)
In rhombus MOTH, angle HTM=(5x+6) degrees. If angle HMO=(12x-6)degrees, what is angle HMO?
Answer:
m∠HMO=102°
Step-by-step explanation:
we know that
In a Rhombus the diagonals bisect the angles and opposite angles are equal
In this problem
Angles HMO and HTO are opposite angles
m∠HMO=m∠HTO
m∠HTM=(1/2)m∠HMO ----> because the diagonals bisect the angles and opposite angles are congruent
substitute the values
[tex](5x+6)\°=(1/2)(12x-6)\°[/tex]
solve for x
[tex]10x+12=12x-6\\12x-10x=12+6\\2x=18\\x=9[/tex]
Find the measure of angle HMO
m∠HMO=(12x-6)°
substitute the value of x
m∠HMO=(12(9)-6)=102°
see the attached figure to better understand the problem
Helen uses 0.12
kilogram of nuts in each batch of granola
that she makes. If she makes 2.5 batches,
how many kilograms of nuts will she use?
Helen uses 0.3 kg of nuts for 2.5 kg of granola.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number.
Given that, Helen uses 0.12 kilogram of nuts in each batch of granola
that she makes, and she makes 2.5 batches,
For 1 batch she uses .12 kg of nuts, so for 2.5 kg she will use = 2.5*0.12 = 0.3 kg
Hence, Helen uses 0.3 kg of nuts for 2.5 kg of granola.
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started a new ixl and i have no idea how to do this
Answer:
y = - [tex]\frac{1}{6}[/tex] x - [tex]\frac{8}{9}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c
Rearrange 3x + 18y = - 16 into this form
Subtract 3x from both sides
18y = - 3x - 16 ( divide all terms by 18 )
y = - [tex]\frac{3}{18}[/tex] x - [tex]\frac{16}{18}[/tex], that is
y = - [tex]\frac{1}{6}[/tex] x - [tex]\frac{8}{9}[/tex] ← in slope- intercept form
Jackie has 6 skirts and 2 dresses. she has brown shoes and black shoes. if each choice is equally likely how much greater is the probability of her choosing a skirt and brown shoes than the probability of her choosing a dress and black shoes?
Answer:
1/2
Step-by-step explanation:
both have equal chances
The required probabilities are 3/8 and 1/8 respectively.
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: Jackie has 6 skirts and 2 dresses.
Total number of dresses=8
Thus the probability of picking a skirt is = 6/8
=3/4
And the probability of picking a dress is =2/8
=1/4
Also, the probability of choosing either shoe is 1/2
Therefore the conditional probability that she chooses a skirt and brown shoes is = 3/4×1/2
=3/8
Similarly Probability( dress+black shoes)=1/4×1/2
=1/8
Hence, The required probabilities are 3/8 and 1/8 respectively.
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A cylinder has a diameter of 6 ft and height of 9 ft. What is the volume of this cylinder?
work plsss
The answer is 254.47 ft
Step-by-step explanation:
V=pi×r^2×h
pi=3.14
r=d/2
r=6/2=3
v=(3.14)×3^2×9
=254.47 ft
Answer:
54ft
Step-by-step explanation:
The formula for volume is base *height
Plz help, It’s kinda easy I’m just kinda dumb ig :( 25+ points
Answer:
Let x = (the height of the fourth plant)
Then the average of the four heights will be:
(70+71+72+x)/4
Simplify it to (213+x)/4
This average has to be at least 73 inches. Meaning, it has to be greater than or equal to 73.
(I don't have the sign for greater/equal so I'll type >=)
(213+x)/4 >= 73
This is the inequality. Just solve for x, and you have the answer.
(213+x) >= 292
x >= 79
Another way: (I think it's easier to do it like this in my head)
You need average 73.
Look at the heights of the plants you have now: how far are they from 73?
The first is 3 less, the second is 2 less, and the third is 1 less.
The 'total deficit'' is 6.
So to make the average be 73, you need to cancel out the deficit by making an equal overage (by 6).
If you can only add one more plant... that plant has to be 6 inches higher than the average you want. So 73+6=79.
Step-by-step explanation:
suppose that 17 inches of wire costs 51 cents. at the same rate, how much ( in cents ) will 33 inches of wire cost?
[tex]\bf \begin{array}{ccll} inches¢s\\ \cline{1-2} 17&51\\ 33&x \end{array}\implies \cfrac{17}{33}=\cfrac{51}{x}\implies 17x=33\cdot 51\implies x = \cfrac{33\cdot 51}{17} \\\\\\ x = 33\cdot \cfrac{51}{17}\implies x = 33\cdot 3\implies x = 99[/tex]
Final answer:
To find the cost of 33 inches of wire, we calculate the cost per inch from the given 17 inches costing 51 cents, which is 3 cents per inch, and then multiply by 33 inches to get a total cost of 99 cents.
Explanation:
The student is asking to determine the cost of 33 inches of wire based on the given rate of 17 inches costing 51 cents. To solve this, we can set up a proportion where we compare the given inches of wire to the given cost and then find the cost for the desired inches of wire.
Step-by-Step Calculation:
First, we determine the cost per inch of wire by dividing the total cost by the total length of wire: 51 cents ÷ 17 inches = 3 cents per inch.
Next, we multiply the cost per inch by the desired length of wire to find the total cost: 3 cents/inch × 33 inches = 99 cents.
Therefore, 33 inches of wire will cost 99 cents at the same rate.
What is .001 as a fraction with a negative exponent.
Answer:
1/1000 or 1x10^(-3)
Step-by-step explanation:
0.001=1/1000 as a fraction
With a negative exponent?
You can write it into standard notation.
It's 1x10^(-3).
0.001 as a fraction with a negative exponent is 10⁻³.
To express the decimal 0.001 as a fraction with a negative exponent, we need to understand how negative exponents work with powers of ten. The decimal 0.001 is equivalent to the fraction [tex]\frac{1}{1000}[/tex], which can be written as [tex]\frac{1}{103}[/tex].
Using the concept of negative exponents, [tex]\frac{1}{103}[/tex] can be rewritten as 10⁻³. This is because a negative exponent indicates the inverse of the corresponding positive exponent. So, 0.001 = 10⁻³.
Summary in Steps:
Convert 0.001 to a fraction: [tex]\frac{1}{1000}[/tex].Express 1/1000 as 10⁻³ using the rule of negative exponents.Therefore, 0.001 equals 10⁻³ as a fraction with a negative exponent.
x² + 4x + 3
How is this solved step by step it needs to be in factored form
Answer:
[tex]\large\boxed{x^2+4x+3=(x+3)(x+1)}[/tex]
Step-by-step explanation:
[tex]x^2+4x+3\\\\\text{We are looking for a and b, for which a + b = 4 and (a)(b) = 3}\\\\\text{a=3,\ b=1}\\\\=x^2+3x+1x+3\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\=x\underbrace{(x+3)}_{(*)}+1\underbrace{(x+3)}_{(*)}\qquad\text{use the distributive property}\\\\=\underbrace{(x+3)}_{(*)}(x+1)[/tex]
Find sin theta if theta is an angle in standard position and the point with coordinates (3, -4) lies on the terminal side of an angle.
Answer:
[tex]\sin \theta=-\frac{4}{5}[/tex]
Step-by-step explanation:
Given:
Angle is in standard position which means the starting ray is at the origin. The terminal side has coordinates (3, -4).
So, the 'x' value is 3 and 'y' value id -4.
Using Pythagoras Theorem, we find the hypotenuse.
Hypotenuse = [tex]\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]
Now, using the sine ratio for the angle, we have
[tex]\sin \theta=\frac{Opposite}{Hypotenuse}\\\sin \theta=\frac{-4}{5}\\\sin \theta=-\frac{4}{5}[/tex]
Therefore, the value of [tex]\sin \theta[/tex] is [tex]-\frac{4}{5}[/tex].
The value is negative as the point (3, -4) lies in the fourth quadrant and sine ratio is negative in the fourth quadrant,
Which expression is equivalent to the given expression? 2(3a+2b−7)
A 5a+4b−5
B 6a+2b−7
C 6a+4b−7
D 6a+4b−14
The expression which is equivalent to the given expression; 2(3a+2b−7) is; 6a +4b -14
Equivalent expressionsThe given expression is;
2(3a+2b−7)Upon expansion by multiplying all elements in the parenthesis by 2; we have;
2(3a+2b−7) = 6a +4b -14Read more on equivalent expressions;
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Final answer:
By distributing the 2 across each term in the expression 2(3a+2b-7), the equivalent expression is 6a + 4b - 14, which corresponds to answer choice D.
Explanation:
To determine which expression is equivalent to 2(3a+2b-7), we need to distribute the 2 across each term in the parentheses. This means we'll multiply 2 by 3a, 2b, and -7 separately. Here's the step-by-step distribution:
2 × 3a = 6a2 × 2b = 4b2 × -7 = -14Combining these results, we get the equivalent expression: 6a + 4b - 14, which matches answer choice D.
Select all irrational numbers.
4√
8√
10√
15√
36√
need help solving this
Answer:
p( <18 years old) =[tex]\frac{72162}{330623}=0.2183=21.83\%[/tex]. Here you evaluate the probability of finding people who are less than 18 years old, by comparing the amount of people who are less than 18 years old (72162), with to the total amount of people in the sample (330623).p( <18 years old /no health insurance)= [tex]\frac{7663}{46340} =0.1654=16.54\%[/tex]. This means that assuming that people does not have insurance (this happens in 46340 cases), in 7663 of this cases, besides not having insurances, the persons are lessthan 18 years old.This events are not independent, because the condition that should hold to obtain independece is that P(<18 years old/ no health insurance)= P(<18 years old), which would mean that, knowing that a person has not health insurance should not add any information to the main fact: that the person's age is below 18. If the equality does not hold, then, knowing that the person has not health insurance helps knowing about the age of the person.
Listed below are the numbers of words spoken in a day by each member of eight different randomly selected couples. Complete parts (a) and (b) below.
Male Female
16,051 24,017
26,378 12,962
1440 17,644
7875 17,399
18,237 12,486
15,728 16,581
14,306 16,533
26,823 18,967
a. Use a 0.05 significance level to test the claim that among couples, males speak fewer words in a day than females.
In this example, mu Subscript d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the words spoken by the male minus words spoken by the female. What are the null and alternative hypotheses for the hypothesis test?
The test statistic is -0.35
The P-value is 0.369
What is the conclusion based on the hypothesis test?
We are testing the claim that males speak fewer words than females. With a p-value of 0.369, which is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, no significant evidence supports the claim that males speak fewer words than females.
Explanation:The objective here is to test the claim that on average, males speak fewer words in a day than females. To do this, we compare two means using a hypothesis test for paired data.
The null hypothesis (H0) is that there is no difference between the mean number of words spoken by males and females. The alternative hypothesis (Ha) is that the mean number of words spoken by males is less than that spoken by females.
Since the p-value (0.369) is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means we do not have significant evidence to support the claim that males speak fewer words than females.
A key takeaway from this is that the test statistic and p-value are critical elements in hypothesis testing. They determine whether or not you have significant evidence to reject the null hypothesis.
Learn more about Hypothesis Testing here:https://brainly.com/question/34171008
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