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Complete Question
A normal population has a mean of 61 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is: (Round z values to 2 decimal places and final answers to 4 decimal places.)
(a) Greater than 64
(b) Less than 57
Answer:
(a) Greater than 64 = 0.1788
(b) Less than 57 = 0.1094
Step-by-step explanation:
To solve the above questions we would be using the z score formula
The formula for calculating a z-score :
z = (x - μ)/σ,
where x is the raw score
μ is the population mean = 61
σ is the population standard deviation = 13
(a) Greater than 64
z = (x - μ)/σ,
where x is 64
μ is the 61
σ is the 13
In the above question, we are given the number of samples = 16
Sample standard deviation = popular standard deviation/ √16
= 13/√16
z = 64 - 61 ÷ 13/√16
z = 3/3.25
z = 0.92308
Approximately, z values to 2 decimal places ≈ 0.92
Using the z score table of normal distribution to find the Probability (P) value of z score of 0.92
P(z = 0.92) = 0.82121
P(x>64) = 1 - P(z = 0.92)
= 1 - 0.82121
= 0.17879
Approximately , Probability value to 4 decimal places = 0.1788
(b) Less than 57
z = (x - μ)/σ,
where x is 57
μ is the 61
σ is the 13
In the above question, we are given the number of samples = 16
Sample standard deviation = popular standard deviation/ √16
= 13/√16
z = 57 - 61 ÷ 13/√16
z = -4/3.25
z = -1.23077
Approximately, z values to 2 decimal places ≈ -1.23
Using the z score table of normal distribution to find the Probability (P) value of z score of -1.23
P(z = -1.23) = P(x<Z) = 0.10935
Approximately , Probability value to 4 decimal places = 0.1094
The length of a rectangle is four times its width. If the perimeter of the rectangle is 50 yd, find its area
Answer:
100yd²
Step-by-step explanation:
length=4x
width=x
perimeter=2(l+w)
50=2(4x+x)
50=2(5x)=10x
50=10x
x=5yd
width=5yd
length=20yd
area=length×width
=20×5
=100yd²
Answer:
[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]
Step-by-step explanation:
width = x
length = 4x
so,
perimeter of a rectangle
[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]
So, in this rectangle,
width = 5 yd
length = 4x
= 4*5
= 20yd
Now, let's find the area of this rectangle
[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]
how many pairs of matching surfaces does a cereal box have
Answer:
3 pairs
Step-by-step explanation:
Top and Bottom
Front and Back
Side and Side.
Cereal Boxes have 6 sides
the product of two consequtive integers is 72 the equation x(x+1)=72 represents the situation, where x represents the smaller integer, which equation can be factor and solve for the smaller integer?
Answer:
x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.
Step-by-step explanation:
Step 1: Distribute x
x² + x = 72
Step 2: Move 72 over
x² + x - 72 = 0
Step 3: Factor
(x - 8)(x + 9) = 0
Step 4: Find roots
x - 8 = 0
x = 8
x + 9 = 0
x = -9
Answer:
x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0
Step-by-step explanation:
Let the first consecutive integer be x.
Let the second consecutive integer be x+1.
The product of the two consecutive integers is 72.
x(x + 1) = 72
x² + x = 72
Subtracting 72 from both sides.
x² + x - 72 = 0
Factor left side of the equation.
(x - 8)(x + 9) = 0
Set factors equal to 0.
x - 8 = 0
x = 8
x + 9 = 0
x = -9
8 and -9 are not consecutive integers.
Try 8 and 9 to check.
x = 8
x + 1 = 9
x(x+1) = 72
8(9) = 72
72 = 72
True!
The two consecutive integers are 8 and 9.
Find the total surface area of the cone in the figure. ( use rr=3.14.)
Answer:
Answer D
Step-by-step explanation:
The formula is [tex]A = pi r(r+\sqrt{h^2+r^2})[/tex]. We have our r (radius) and h (height), so plugging it all in would give us A = (3.14)(5 + sqrt(12^2)+(5^2). After computing this, you would get answer D, 282.6.
?? help out plssss ill do the thing wtv its called
Steps to solve:
1 = -4 + 3/8x
~Add 4 to both sides
1 + 4 = -4 + 4 + 3/8x
~Simplify
5 = 3/8x
~Multiply 8/3 to both sides
5 * 8/3 = 3/8x * 8/3
~Simplify
13 1/3 = x
As we look through the answer choices, we can see that none resembles any of the steps I did above but by looking at the answers for each one, the only logical answer is B since it has a final answer of x = 40/3 or 13 1/3.
Best of Luck!
As the Type II error, β,of a statistical test increases, the power of the test _____________.
Answer:
decreases.
Step-by-step explanation:
Type II error is one in which we fail to reject the null hypothesis that is actually false. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The power of Type II error is 1 - [tex]\beta[/tex]. As the power increases the probability of Type II error decreases.
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 60%. You would like to be 98% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required?
Answer:
A sample size of 2080 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
Based on previous evidence, you believe the population proportion is approximately 60%.
This means that [tex]\pi = 0.6[/tex]
How large of a sample size is required?
We need a sample of n.
n is found when [tex]M = 0.025[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.025 = 2.327\sqrt{\frac{0.6*0.4}{n}}[/tex]
[tex]0.025\sqrt{n} = 2.327\sqrt{0.6*0.4}[/tex]
[tex]\sqrt{n} = \frac{2.327\sqrt{0.6*0.4}}{0.025}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.327\sqrt{0.6*0.4}}{0.025})^{2}[/tex]
[tex]n = 2079.3[/tex]
Rounding up
A sample size of 2080 is needed.
An exterior angle of a triangle is 120° and one of the interior opposite angle is 50°. Find the other two angles of the triangle.
Answer:
interior angle (2)= 70
interior angle (3)= 60
Step-by-step explanation:
Given:
exterior angle=120°
interior angle (1)=50°
Required:
interior angle (2)=?
interior angle (3)=?
Formula:
exterior angle=interior angle (1) + interior angle (2)
Solution:
exterior angle=interior angle (1)+ interior angle (2)
120°=50°+interior angle (2)
120°+50°=interior angle (2)
70°=interior angle (2)
interior angle (3)= 180°-interior angle (1)- interior angle (2)
interior angle (3)=180°-50°+70°
interior angle (3)=180°-120°
interior angle (3)= 60°
Theorem:
Theorem 1.16
The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
Hope this helps ;) ❤❤❤
The value of y varies inversely as the square of x, and y = 16, when I = 3.
Find the value of x when y = 1.
Answer:
x = 12Step-by-step explanation:
The statement
The value of y varies inversely as the square of x is written as
[tex]y = \frac{k}{ {x}^{2} } [/tex]
where k is the constant of proportionality
To find the value of x when y = 1 first find the formula for the variation
y = 16 x = 3
k = yx²
k = 16(3)²
k = 16 × 9
k = 144
The formula for the variation is
[tex]y = \frac{144}{ {x}^{2} } [/tex]
when y = 1
We have
[tex]1 = \frac{144}{ {x}^{2} } [/tex]
Cross multiply
x² = 144
Find the square root of both sides
We have the final answer as
x = 12Hope this helps you
What is the equation for the plane illustrated below?
Answer:
Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].
Step-by-step explanation:
The general equation in rectangular form for a 3-dimension plane is represented by:
[tex]a\cdot x + b\cdot y + c\cdot z = d[/tex]
Where:
[tex]x[/tex], [tex]y[/tex], [tex]z[/tex] - Orthogonal inputs.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex], [tex]d[/tex] - Plane constants.
The plane presented in the figure contains the following three points: (2, 0, 0), (0, 2, 0), (0, 0, 3)
For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:
xy-plane (2, 0, 0) and (0, 2, 0)
[tex]y = m\cdot x + b[/tex]
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - x-Intercept, dimensionless.
If [tex]x_{1} = 2[/tex], [tex]y_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]y_{2} = 2[/tex], then:
Slope
[tex]m = \frac{2-0}{0-2}[/tex]
[tex]m = -1[/tex]
x-Intercept
[tex]b = y_{1} - m\cdot x_{1}[/tex]
[tex]b = 0 -(-1)\cdot (2)[/tex]
[tex]b = 2[/tex]
The equation of the line in the xy-plane is [tex]y = -x+2[/tex] or [tex]x + y = 2[/tex], which is equivalent to [tex]3\cdot x + 3\cdot y = 6[/tex].
yz-plane (0, 2, 0) and (0, 0, 3)
[tex]z = m\cdot y + b[/tex]
[tex]m = \frac{z_{2}-z_{1}}{y_{2}-y_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
If [tex]y_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]y_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:
Slope
[tex]m = \frac{3-0}{0-2}[/tex]
[tex]m = -\frac{3}{2}[/tex]
y-Intercept
[tex]b = z_{1} - m\cdot y_{1}[/tex]
[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]
[tex]b = 3[/tex]
The equation of the line in the yz-plane is [tex]z = -\frac{3}{2}\cdot y+3[/tex] or [tex]3\cdot y + 2\cdot z = 6[/tex].
xz-plane (2, 0, 0) and (0, 0, 3)
[tex]z = m\cdot x + b[/tex]
[tex]m = \frac{z_{2}-z_{1}}{x_{2}-x_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - z-Intercept, dimensionless.
If [tex]x_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:
Slope
[tex]m = \frac{3-0}{0-2}[/tex]
[tex]m = -\frac{3}{2}[/tex]
x-Intercept
[tex]b = z_{1} - m\cdot x_{1}[/tex]
[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]
[tex]b = 3[/tex]
The equation of the line in the xz-plane is [tex]z = -\frac{3}{2}\cdot x+3[/tex] or [tex]3\cdot x + 2\cdot z = 6[/tex]
After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:
[tex]a = 3[/tex], [tex]b = 3[/tex], [tex]c = 2[/tex], [tex]d = 6[/tex]
Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].
Answer:
It is A 3x+3y+2z=6
Step-by-step explanation:
A stained-glass window is shaped like a right triangle. The hypotenuse is 15feet. The length of one leg is three more than the other. Find the lengths of the legs.
let us build equation for unknown legs
If we keep the length pf one leg as x
the other leg would be x +3
so we can build a relationship using pythagoras theorem
x^2 + (x+3)^2 = 15^2
x^2 + x^2 + 6x + 9 = 225
2x^2 + 6x + 9 = 225
2x^2 + 6x+ 9-225 = 0
2x^2 + 6x - 216 = 0
x^2 + 3x - 108 = 0 dividing whole equation by 2
x^2 + 12x - 9x - 108 = 0
x ( x + 12 ) - 9 (x + 12) = 0
(x -9) ( x +12) = 0
solutions for x are
x = 9 or x = -12
as lengths cannot be negative
one side length is 9cm
and other which is( x + 3)
9 + 3
12cm
The lengths of the legs of the right angled triangle is 9 feet and 12 feet.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:
Hypotenuse² = First Leg² + Second leg²
Let x represent the length of one leg. The other leg is three more = x + 3, hypotenuse = 15 ft. Hence:
15² = x² + (x + 3)²
x² + 6x + 9 + x² = 225
2x² + 6x - 216 = 0
x² + 3x - 108 = 0
x = - 12 or x = 9
Since the length cant the negative hence x= 9, x + 3 = 12
The lengths of the legs of the right angled triangle is 9 feet and 12 feet.
Find out more at: https://brainly.com/question/10040532
Which steps can be used in order to determine the solution to Negative 1.3 + 4.6 x = 0.3 + 4 x?
Answer:
x=8/3 OR 2.7
Step-by-step explanation:
-1.3+4.6x=0.3+4x
4.6x-4x=0.3+1.3
0.6x=1.6
x=1.6/0.6=8/3
x=8/3 OR 2.7
Hope this helps!
Answer:
[tex]\boxed{x = 2\frac{2}{3} }[/tex]
Step-by-step explanation:
[tex]-1.3+4.6x = 0.3 +4x[/tex]
Collecting like terms
[tex]4.6 x -4x = 0.3+1.3[/tex]
[tex]0.6x = 1.6[/tex]
Dividing both sides by 0.6
x = 1.6 / 0.6
x = 2 2/3
The board of directors of Midwest Foods has declared a dividend of $3,500,000. The company has 300,000 shares of preferred stock that pay $2.85 per share and 2,500,000 shares of common stock. After finding the amount of dividends due the preferred shareholders, calculate the dividend per share of common stock.
Answer:
$855,000Dividend per share of common stock = $1.06Step-by-step explanation:
1. Preferred Share dividends.
There are 300,000 preference shares and each of them got $2.85. Total dividends are;
= 300,000 * 2.85
= $855,000
2. Total dividends = $3,500,000
Dividends left for Common Shareholders (preference gets paid first)
= 3,500,000 - 855,000
= $2,645,000
Common shares number 2,500,000
Dividend per share of common stock = [tex]\frac{2,645,000}{2,500,000}[/tex]
= $1.06
Line AB and Line CD are parallel lines. Which translation of the plane can we use to prove angles x and y are congruent, and why?
Answer:
Option C.
Step-by-step explanation:
In the given figure we have two parallel lines AB and CD.
A transversal line FB intersect the parallel lines at point B and C.
We know that the if a transversal line intersect two parallel lines, then corresponding angles are congruent.
[tex]\angle ABC=\anle ECF[/tex]
[tex]x=y[/tex]
To prove this by translation, we need a translation along the directed line segment CB maps ine CD onto line AB and angle y onto angle x.
Therefore, the correct option is C.
An investigation of a number of automobile accidents revealed the following information:
18 accidents involved alcohol and excessive speed.
26 involved alcohol.
12 accidents involved excessive speed but not alcohol.
21 accidents involved neither alcohol nor excessive speed.
How many accidents were investigated?
Answer:
59 accidents were investigated.
Step-by-step explanation:
The question above is a probability question that involves 2 elements: causes of accidents.
Let
A = Alcohol
E = Excessive speed
In the question, we are given the following information:
18 accidents involved Alcohol and Excessive speed =P(A ∩ E)
26 involved Alcohol = P(A)
12 accidents involved excessive speed but not alcohol = P( E ) Only
21 accidents involved neither alcohol nor excessive speed = neither A U B
We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)
P(A Only) = 26 - 18
= 8
So, only 8 accident involved Alcohol but not excessive speed.
The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)
= 8 + 12 + 18 + 21
= 59
Therefore, 59 accidents were investigated.
Find the exact values of sin 2θ and cos 2θ for cos θ = 6/13
Answer:
Step-by-step explanation:
cos^-1(6/13)=62.5136°
sin(2*62.5136°)=0.8189
cos(2*62.5136°)=-0.5740
The radius of a nitrogen atom is 5.6 × 10-11 meters, and the radius of a beryllium atom is 1.12 × 10-10 meters. Which atom has a larger radius, and by how many times is it larger than the other?
Answer:
The beryllium atom; 1.99 times larger.
Step-by-step explanation:
The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.
(1.12 * 10^-10) / (5.6 * 10^-11)
= (1.112 / 5.6) * (10^-10 + 11)
= 0.1985714286 * 10
= 1.985714286 * 10^0
So, the beryllium atom is about 1.99 times larger than the other.
Hope this helps!
Please answer this correctly without making mistakes
Answer:
41.1 miles
Step-by-step explanation:
84 - 42.9 = 41.1
helpppppppppppppppppppppppppppppp
Answer:
0
Step-by-step explanation:
Hope this helps
A survey of 700 non-fatal car accidents showed that 183 involved faulty equipment. Find a point estimate for the population proportion of non-fatal car accidents that involved faulty equipment.
Answer:
Point of faulty equipment car = 0.2614 (Approx)
Step-by-step explanation:
Given:
Total number of car = 700
Faulty equipment car = 183
Find:
Point of faulty equipment car
Computation:
Point of faulty equipment car = Faulty equipment car / Total number of car
Point of faulty equipment car = 183 / 700
Point of faulty equipment car = 0.261428571
Point of faulty equipment car = 0.2614 (Approx)
WILL GIVE YOU BRAINLIEST
Answer:
AB = 20 tan55°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{20}[/tex] ( multiply both sides by 20 )
20 tan55° = AB
20 points please help!!!
Answer:
a = 16
b = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Length of the design 16 inches is represented by the point (0, 16) and length of 12 inches by (1, 12).
That means these points lie on the graph of the function 'f' represented by,
f(x) = a(b)ˣ
For the point (0, 16),
f(0) = a(b)⁰
16 = a(1)
a = 16
For another point (1, 12),
f(1) = a(b)¹
12 = ab
12 = 16(b) [Since a = 16]
b = [tex]\frac{12}{16}[/tex]
b = [tex]\frac{3}{4}[/tex]
Therefore, values of a and b are 16 and [tex]\frac{3}{4}[/tex] respectively.
Find a power series for the function, centered at c. f(x) = 1 9 − x , c = 4 f(x) = [infinity] n = 0 Incorrect: Your answer is incorrect. Determine the interval of convergence. (Enter your answer using interval notation.)
Looks like the given function is
[tex]f(x)=\dfrac1{9-x}[/tex]
Recall that for |x| < 1, we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
We want the series to be centered around [tex]x=4[/tex], so first we rearrange f(x) :
[tex]\dfrac1{9-x}=\dfrac1{5-(x-4)}=\dfrac15\dfrac1{1-\frac{x-4}5}[/tex]
Then
[tex]\dfrac1{9-x}=\displaystyle\frac15\sum_{n=0}^\infty\left(\frac{x-4}5\right)^n[/tex]
which converges for |(x - 4)/5| < 1, or -1 < x < 9.
What is the solution for x in the given equation? (root)9x+7+ (root)2x=7 A. x = 18 and x = 2 B. x = 18 C. x = 2 D. x = 18 and x = -2
Answer:
C. x = 2
Step-by-step explanation:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
Since you have square roots, you need to separate the square roots and square both sides.
[tex] \sqrt{9x + 7} = 7 - \sqrt{2x} [/tex]
Now that one square root is on each side of the equal sign, we square both sides.
[tex] (\sqrt{9x + 7})^2 = (7 - \sqrt{2x})^2 [/tex]
[tex] 9x + 7 = 49 - 14\sqrt{2x} + 2x [/tex]
Now we isolate the square root and square both sides again.
[tex] 7x - 42 = -14\sqrt{2x} [/tex]
Every coefficient is a multiple of 7, so to work with smaller numbers, we divide both sides by 7.
[tex] x - 6 = -2\sqrt{2x} [/tex]
Square both sides.
[tex] (x - 6)^2 = (-2\sqrt{2x})^2 [/tex]
[tex] x^2 - 12x + 36 = 4(2x) [/tex]
[tex] x^2 - 20x + 36 = 0 [/tex]
We need to try to factor the left side.
-2 * (-18) = 36 & -2 + (-18) = -20, so we use -2 and -18.
[tex] (x - 2)(x - 18) = 0 [/tex]
[tex] x = 2 [/tex] or [tex] x = 18 [/tex]
Since solving this equation involved the method of squaring both sides, we much check for extraneous solutions by testing our two solutions in the original equation.
Test x = 2:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(2) + 7} + \sqrt{2(2)} = 7 [/tex]
[tex] \sqrt{25} + \sqrt{4} = 7 [/tex]
[tex] 5 + 2 = 7 [/tex]
[tex] 5 = 5 [/tex]
We have a true equation, so x = 2 is a true solution of the original equation.
Now we test x = 18.
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(18) + 7} + \sqrt{2(18)} = 7 [/tex]
[tex] \sqrt{162 + 7} + \sqrt{36} = 7 [/tex]
[tex] \sqrt{169} + 6 = 7 [/tex]
[tex] 13 + 6 = 7 [/tex]
[tex] 19 = 7 [/tex]
Since 19 = 7 is a false equation, x = 18 is not a true solution of the original equation and is discarded as an extraneous solution.
Answer: C. x = 2
I made a square frame for my favorite bird picture from four wooden pieces. Each piece is a rectangle with a perimeter of 24 inches. What is the area and perimeter of the picture and frame, together?
Answer:
Perimeter of the picture and frame = 38.4inches
Area of the picture and frame = 92.16inches²
Step-by-step explanation:
A square frame is made up of 4 different pieces. The shape of each piece = Rectangle
The perimeter of the rectangle = 24
Perimeter of the rectangle = 24 inches
The perimeter of a rectangle = 2L + 2W
The Width of a Rectangle is always on her than the length hence.
24 = 2L + 2W
24 = 2( L + W)
24/2 = L + W
12 = L + W
Because the width is always longer than the length
W > L
Width of wooden frame = 4 × Length
Therefore;
4 × L = W
Which gives
L + W = 12 inches
4 × L + L = 12 inches
L×(4 + 1)
= 5L = 12 inches
L = 12/5 = 2.4 inches
W = 4 × L = 4 × 12/5
W = 48/5 = 9.6 inches
Side length of wooden frame, L =9.6
The perimeter of the picture frame = 4 × L= 4 × 9.6= 38.4 inches
The area of the picture frame = L²
= L × L
= 9.6 × 9.6 = 92.16inches².
Solve for x 90°, 45°, and x°
Answer:
x= 45
Step-by-step explanation:
In this diagram, there is an angle that is split into 2 angles.
The angle is a 90 degree angle. We know this because of the little square in the corner that denotes a right angle.
Therefore, the 2 angles inside of the right angle must add to 90 degrees. The 2 angles that make up the right angle are x and 45.
x+45=90
We want to find x. We need to get x by itself. 45 is being added on to x. The inverse of addition is subtraction. Subtract 45 from both sides.
x+45-45=90-45
x= 90-45
x=45
The measure of angle x is 45 degrees.
x−15≤−6 solve for x pls help
Answer:
x≤9
Step-by-step explanation:
x−15≤−6
Add 15 to each side
x−15+15≤−6+15
x≤9
Answer:
[tex]\boxed{x\leq 9}[/tex]
Step-by-step explanation:
[tex]x-15 \leq -6[/tex]
[tex]\sf Add \ 15 \ to \ both \ parts.[/tex]
[tex]x-15 +15 \leq -6+15[/tex]
[tex]x\leq 9[/tex]
Which phrase best describes the graph of a proportional relationship?
A) a straight line passing
B) a straight line
C) a curve
D) not a straight line
Answer:
A. a straight line passing
Step-by-step explanation:
Answer:
a straight line passing
Step-by-step explanation:
Betty and Karen have been hired to paint the houses in a new development. Working together, the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 14 h to paint a house alone. Betty takes 6 h to paint a house alone.
Required:
How long does it take Karen to paint a house working alone?
Answer: 3 hours
Step-by-step explanation:
Here is the correct question:
Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 6 hours to paint a house alone. How long does it take karen to paint a house working alone?
Since Betty takes 6 hours to paint a house alone, that means she can paint 1/6 of the house in 1 hour.
Karen can also paint 1/x in 1 hour
Both of them will paint the house in 3/2 hours.
We then add them together which gives:
1/6 + 1/x = 3/2x
The lowest common multiple is 6x
1x/6x + 6/6x = 9/6x
We then leave out the denominators
1x + 6 = 9
x = 9 - 6
x = 3
Karen working alone will paint a house in 3 hours.
Math question, need help
In general, if we have [tex]x^a=x^b,[/tex] then [tex]a=b.[/tex] Thus, the first answer choice is correct.
Answer:
[tex]\boxed{\red{2x - 1 = 5x - 14}}[/tex]
First answer is correct.
Step-by-step explanation:
we know that,
[tex] {x}^{a} = {x}^{b} [/tex]
[tex]a = b[/tex]
So, according to that,
[tex] {5}^{(2x - 1)} = {5}^{(5x - 14)} [/tex]
Therefore,
[tex]2x - 1 = 5x - 14[/tex]