Answer:
17.3 Inches
Step-by-step explanation:
Given that the diagonal of a cube = 30 inches
For a cube of side length s, Length of its diagonal [tex]=s\sqrt{3}[/tex]
Therefore:
[tex]s\sqrt{3}=30\\$Divide both sides by \sqrt{3}\\s=30 \div \sqrt{3}\\s=17.3$ inches (to the nearest tenth.)[/tex]
Side Length of the cube is 17.3 Inches.
Answer:
17.3
Step-by-step explanation:
Edge 2020
Please help this is urgent!
Answer:
Isosceles
Obtuse
Step-by-step explanation:
1) When two sides of a triangle are the same length, the triangle is an isosceles triangle.
2) When one angle of the triangle is greater than 90 degrees, the triangle is an obtuse triangle.
I hope this helps! Have a great day!
Answer:
Isosceles, obtuse
Step-by-step explanation:
There are three types of triangles based on their sides:
Equilateral: a triangle with 3 equal sidesIsosceles: a triangle with 2 equal sidesScalene: a triangle with no equal sidesThis triangle here as sides of 28 cm, 16 cm, and 16 cm
This triangle has two equal sides of 16 cm, indicating it is an isosceles triangleThere are three types of triangles based on their angles:
Acute: when all angles are less than 90° Right: when the triangle has one angle that is 90° Obtuse: when one of the angles is greater than 90°This triangle has angles of 26°, 26°, and 128°
This triangle has one angle that is greater than 90° → 128°, indicating that this is an obtuse triangleAmong 21- to 25-year-olds, 29% say they have driven while under the influence of alcohol. Suppose that three 21- to 25-year-olds are selected at random. a)What is the probability that all three have driven while under the influence of alcohol
Answer:
P(3) = 0.0244
P(3) = 2.44%
the probability that all three selected have driven while under the influence of alcohol is 2.44% or 0.0244
Step-by-step explanation:
Given;
The probability that they have driven while under the influence of alcohol is;
P = 29% = 0.29
the probability that all three selected have driven while under the influence of alcohol is;
P(3) = P × P × P
P(3) = 0.29 × 0.29 × 0.29
P(3) = 0.024389
P(3) = 0.0244
P(3) = 2.44%
the probability that all three selected have driven while under the influence of alcohol is 2.44% or 0.0244
Which of the following linear equations has the steepest slope?
A. Y = -2x +11
B. y=+x+4
C. y - x +7
D. y - 7+2
Answer:
A --- unless d is supposed to be "y= -7x + 2"
Step-by-step explanation:
The slope is m in y=mx + b
So:
a. y= -2x + 11 slope= -2
b. y= x + 4 slope= 1
c. y= -x + 7 slope= -1
d. y= -7 + 2 (I don's see an x but if there were an x I assume that the slope would equal -7)
The higher the m value, the steeper the slope because it is m/1
So, -2/1 is steeper than 1/1 or -1/1
2x+3=-7 twenty Chanda long-standing look
Answer:
x =-5
Step-by-step explanation:
Answer:
x=-5
Step-by-step explanation:
Please answer this correctly
Answer:
Opinion
Step-by-step explanation:
This is an opinion because it says "more exciting to visit than"
This implies the persons' own beliefs and is not a fact, because this is not true for everyone
(x-5)(x+1)=x-5 3(x+1) 3 For what values of x are the two expressions equal ?
Answer:
x=-77+5√ 231 x=-77-5√231
I got this answer for x and the both equations are equal
if log3(x+1) - log3x=2, then x = ?
Answer:
x= 1/8
Step-by-step explanation:
Bonita said that the product of 5/6 x 1 2/3 is 7/3. How can you tell that her answer is wrong.
Answer:=
1 7/18
Step-by-step explanation:
Turn the improper fraction into a mixed fraction.
A state end-of-grade exam in American History is a multiple-choice test that has 50 questions with 4 answer choices for each question. A student must get at least 25 correct to pass the test, and the questions are very difficult. Question 1. If a student guesses on every question, what is the probability the student will pass
Answer:
0.004% probability the student will pass
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 50, p = \frac{1}{4} = 0.25[/tex]
So
[tex]\mu = E(X) = np = 50*0.25 = 12.5[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.25*0.75} = 3.06[/tex]
If a student guesses on every question, what is the probability the student will pass
Using continuity correction, this is [tex]P(X \geq 25 - 0.5) = P(X \geq 24.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 24.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24.5 - 12.5}{3.06}[/tex]
[tex]Z = 3.92[/tex]
[tex]Z = 3.92[/tex] has a pvalue of 0.99996
1 - 0.99996 = 0.00004
0.004% probability the student will pass
find the area of this figure to the nearest hundredth use 3.14 to approximate pi A=? ft squared
Answer:
[tex]105.13ft^2[/tex]
Step-by-step explanation:
Rectangle
[tex]A=lw\\=10*8\\=80ft^2\\[/tex]
Semicircle
[tex]A=\frac{1}{2} \pi r^2\\=\frac{1}{2}* \pi *4^2\\=25.13ft^2[/tex]
Add both values together
[tex]80+25.13\\=105.13ft^2[/tex]
Answer: 105.13
Step-by-step explanation:
One number is 4 plus one half of another number. Their sum is 31. Find the numbers.
Answer:
18, 13
Step-by-step explanation:
x=4+1/2y
x+y=31
4+1/y+y=31
3/2y=27
y=18
x=31-18=13
Answer:
13 & 18
Step-by-step explanation:
Create the formulas:
0.5x+4=y
x+y=31
0.5x+4=y
Multiply both sides by 2
x+8=2y
x+y=31
Subtract 31 from both sides
x+y-31=0
Subtract y from both sides
x-31= -y
Multiply both sides by -1
-x+31=y
Multiply both sides by 2
-2x+62=2y
Combine equations:
-2x+62=x+8
Add 2x to both sides
62=3x+8
Subtract 8 from both sides
3x=54
Divide both sides by 3
x=18
0.5x+4=y
Subtract y from both sides
0.5x-y+4=0
Subtract 0.5x from both sides
-y+4= -0.5x
Multiply both sides by -1
y-4=0.5x
Multiply both sides by 2
2y-8=x
x+y=31
Subtract y from both sides
x= -y+31
Combine equations:
2y-8= -y+31
Add y to both sides
3y-8=31
Add 8 to both sides
3y=39
Divide both sides by 3
y=13
Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.
60
25
Answer:
65
Step-by-step explanation:
C^2= A^2 + B^2
C^2 = (60)^2 + (25)^2
C^2 = 4225
Take the square root of C
C = 65
Answer:
65
Step-by-step explanation:
Use the Pythagorean Theorem to find the length of the hypotenuse.
[tex]a^2+b^2=c^2[/tex]
I'm assuming that '60' and '25' are measures of the legs, since the question asks to find the hypotenuse.
[tex]60^2+25^2=c^2\\\rightarrow 60^2=3600\\\rightarrow 25^2 = 625\\3600+625=c^2\\4225=c^2\\\sqrt{4225}=\sqrt{c^2}\\\boxed{65=c}[/tex]
The hypotenuse should measure 65 units.
Which expression is equivalent to 36 a minus 27?
9 (4 a minus 3)
3 (18 a minus 9)
9 (4 a minus 27)
3 (12 a minus 6)
Answer:
[tex]9(4a)-9(3)[/tex]
Step-by-step explanation:
[tex]36a-27[/tex]
[tex]9(4a)-9(3)[/tex]
[tex]9(4a-3)[/tex]
Answer:
it is 9(4a-3)
Step-by-step explanation:
Please help me with this problem I am lost
Answer:
[tex]\frac{49}{15}[/tex]
Step-by-step explanation:
[tex]\frac{2}{5} \times \frac{7}{-6} \times -7[/tex]
[tex]\frac{2}{5} \times \frac{7}{-6} \times \frac{-7}{1}[/tex]
[tex]\frac{2 \times 7 \times -7}{5 \times -6 \times 1}[/tex]
[tex]\frac{-98}{-30}=\frac{98}{30}=\frac{49}{15}[/tex]
Answer:
-3.26 repeating
Step-by-step explanation:
2×7=14
5×(-6) = -30
14/30×(-7)= -3.26 repeating
choose the most convenient method to graph the line y=−3
Answer:
the line just goes straight up the y-axis. so, place your dot at -3 and draw the line straight up
Step-by-step explanation:
The line is shifted downward by 3 units from the x-axis, and the slope of the line is zero. The intercept of the line is at (0, -3).
What is the graph of the function?The collection of all coordinates in the planar of the format [x, f(x)] that make up a variable function's graph.
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equation of the line is given below.
y = –3
The line y = –3 is parallel to the x-axis.
The slope of the line is zero.
The line is shifted downward by 3 units from the x-axis.
The intercept of the line is at (0, -3).
The graph of the line y = –3 is given below.
More about the graph of the function link is given below.
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According to the Bureau of Labor Statistics, 7.1% of the labor force in Wenatchee, Washington was unemployed in February 2019. A random sample of 100 employable adults in Wenatchee, Washington was selected. Using the normal approximation to the binomial distribution, what is the probability that 6 or more people from this sample are unemployed
Answer:
73.24% probability that 6 or more people from this sample are unemployed
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 100, p = 0.071[/tex]
So
[tex]\mu = E(X) = np = 10*0.071 = 7.1[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.071*0.929} = 2.5682[/tex]
What is the probability that 6 or more people from this sample are unemployed
Using continuity correction, this is [tex]P(X \geq 6 - 0.5) = P(X \geq 5.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 5.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5.5 - 7.1}{2.5682}[/tex]
[tex]Z = -0.62[/tex]
[tex]Z = -0.62[/tex] has a pvalue of 0.2676
1 - 0.2676 = 0.7324
73.24% probability that 6 or more people from this sample are unemployed
Tricia has a birthday party. During the party, she opened 36 gifts, which was 60% of all her gifts. After the party, she opened the rest of the gifts and found that 25% of them were the same present, so she returned all but one of the duplicate gifts. How many gifts did she return?
Answer:
She returned 5 gifts.
Step-by-step explanation:
36 gifts is 60% = 0.6 of all the gifts that she received. How many presents are 100% = 1?
36 gifts - 0.6
x gifts - 1
0.6x = 36
x = 36/0.6
x = 60
She received 60 gifts.
She opened the rest of the gifts and found that 25% of them were the same present
The rest is 60 - 36 = 24 gifts.
25% is (1/4)*24 = 6 duplicate figts
She returned all but one of the duplicate gifts.
That is, she returned 6 - 1 = 5 gifts.
If a⊕ b= 1/a + 1/b , for what decimal value of a is a⊕ 0.2=10?
Answer:
0.2
Step-by-step explanation:
1/0.2 = 5
10-5 = 5
1/a = 5
a = 1/5
a = 0.2
Answer:1/5 or 0.2
Step-by-step explanation:
1/a+1/0.2=10
1/a+1/2/10=10
1/a=10/2=10
1/a+5=10
1/a=10-5
1/a=5
a=1/5 or 0.2
what is 0.035 as a simplified reduced fraction
Answer:
7/200
Step-by-step explanation:
0.035= 35/1000= 7*5/200*5=7/200
The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x)
= 9x - 2. Which expression represents the profit, (k-h(x), of producing soccer balls?
Answer:
4x - 8
Step-by-step explanation:
k - H(x)
(9x -2) - (5x + 6)
4x -8
Maria has $39.00 that she can spend on school supplies. If she spends $18.00 on pens and pencils, how many packs of notebook paper can she buy if the notebook paper costs $3.00 a pack, including tax? Choose the graph that shows your answer.
Answer:
Please show the graph choice it sounds linear xy (positive)
or parallel depending on how much pens and pencils were.
We know $18 purchased more than 1 pack so this divided by notebook shws us at least 6 per notepack paper or so many packs of pen that cost $18 ffor pens were ratio to 1 pack of paper. ie) if pens were £2 pack then while we understand it could have been as many as 9 we divide by how many we find or bought by the amount of notepaper books to determine the rate and distribution of the money.
Step-by-step explanation:
$39 - $18 = $21 left over
21/3 = 7 packs of note paper can be purchased..
Find the nth term and the 150th term of the following sequence 7,11,15,19,23,...
Answer:
for the 9th it is 39 for the 150th it is 607
What is the equation of the line perpendicular to y = 2/3 x +1 that passes through the point (12, – 6)?
Answer:
y= -3/2x+12
Step-by-step explanation:
the slope of perpendicular lines multiplied together would be -1, so the slope of the perpendicular line is -3/2. y=-3/2x+b, so -6=-18+b, so b= 12. the equation of the line is y=-3/2x+12.
You are at a playground with a see-saw and a large merry-go-round. You put your phone on the see-saw and find it slides when it is tilted at an angle of 38 degrees. How far can you put your phone from the center of the merry-go-round (in m) when it makes one rotation every 3 s
Answer: r_max = 1.75m
Step-by-step explanation:
Below is a rather brief analysis to solving this problem.
The phone starts sliding when along incline,
when F_net = m g sin(theta) - fs_max = 0
and fs_max = us N = us m g cos(theta)
m g sin(theta) - us m g cos(theta) =
us = tan(theta) = tan38 = 0.781
On merry - go - round,
fs_max = us N = us m g
Using F = m a
fs_max = m w^2 r_max and w = 2pi / T
us m g = m (2 pi / T)^2 (r_max)
0.781 x 9.81 = (2 pi / 3)^2 (r_max)
r_max = 1.75 m
cheers i hope this helped !!
What is the value of the trig ratio cos x ? Help ASAP
Answer:
14/50 or 7/25
Step-by-step explanation:
cos x = adj/hyp
adj = 14
hyp = 50
---------
you ca learn more about trig
sin x = opp/hyp
tan x = opp/adj
The value of the trigonometric ratio, cos x in a right angle triangle XYZ is [tex]\dfrac{14}{50}[/tex].
Trigonometric ratios – The relation between the angles and the sides of a right-angle triangle is called Trigonometric ratios.
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In the given figure a right-angle triangle XYZ we know that
ZY is the length of the perpendicular. XY is the base of the triangle and ZX is the hypotenuse.
By trigonometric ratio, we know that
[tex]Cos \Theta = \dfrac{adjacent}{hypotenuse}[/tex]
Where [tex]\Theta[/tex] is the acute angle between the base and the Hypotenuse
On substituting value,
[tex]Cos \Theta = \dfrac{14}{50}[/tex]
The value of the trigonometric ratio, cos x in a right angle triangle XYZ [tex]\dfrac{14}{50}[/tex].
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Suppose that a large mixing tank initially holds 100 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 4 lb/gal, determine a differential equation (in lb/min) for the amount of salt A(t) (in lb) in the tank at time t > 0. (Use A for A(t).)
Answer:
dA/dt = 12 - 2A/(100 + t)
Step-by-step explanation:
The differential equation of this problem is;
dA/dt = R_in - R_out
Where;
R_in is the rate at which salt enters
R_out is the rate at which salt exits
R_in = (concentration of salt in inflow) × (input rate of brine)
We are given;
Concentration of salt in inflow = 4 lb/gal
Input rate of brine = 3 gal/min
Thus;
R_in = 4 × 3 = 12 lb/min
Due to the fact that solution is pumped out at a slower rate, thus it is accumulating at the rate of (3 - 2)gal/min = 1 gal/min
So, after t minutes, there will be (100 + t) gallons in the tank
Therefore;
R_out = (concentration of salt in outflow) × (output rate of brine)
R_out = [A(t)/(100 + t)]lb/gal × 2 gal/min
R_out = 2A(t)/(100 + t) lb/min
So, we substitute the values of R_in and R_out into the Differential equation to get;
dA/dt = 12 - 2A(t)/(100 + t)
Since we are to use A foe A(t), thus the Differential equation is now;
dA/dt = 12 - 2A/(100 + t)
Given a quadratic function that has solutions at x=4 and x=6 which of the following is one of the linear factors of the function?
A.(x+4)
B.(x-6)
C.(x-2)
D.(x+6)
Answer: THE SOLUTION IS B
x=4 gives the linear factor x-4
x=6 gives the linear factor x-6
Step-by-step explanation:
Nathan spins 2 different spinners at the same time.There are a total of 10 possible outcomes.which pair of spinners did Nathan spin?
Answer:
The one divided into five part and the one divided into two parts
Step-by-step explanation:
find the option with one that has five parts and one with two parts :3
hope this helps!!
It is the graph with 5 numbers and 5 letters
I ready diagnostic
help solve the above equation
Answer:
[tex]\dfrac{1}{27}[/tex]
Step-by-step explanation:
[tex]n^{-\frac{2}{3}}=9[/tex]
Rewrite:
[tex]\dfrac{1}{\sqrt[3]{n^2}}=9\\\\9\sqrt[3]{n^2}=1[/tex]
Cube both sides:
[tex]729n^2=1[/tex]
Divide both sides by 729:
[tex]n^2=\dfrac{1}{729}[/tex]
Take the square root of both sides:
[tex]n=\sqrt{\dfrac{1}{729}}=\dfrac{1}{27}[/tex]
Hope this helps!
Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many real number
solutions does the equation have?
Discriminant = b2-4ac
0
1
2
o 12
Save and Exit
Next
Submit
Mark this and return
le
Step-by-step explanation:
work is shown and pictured
The discriminant of quadratic equation is,
⇒ D = 0
What is Quadratic equation?
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form: ax² + bx + c = 0
We have to given that;
Quadratic equation is,
⇒ - 3 = x² + 4x + 1
Now, We can write as;
⇒ x² + 4x + 1 + 3 = 0
⇒ x² + 4x + 4 = 0
Hence, Discriminant of quadratic equation is,
⇒ D = b² - 4ac
⇒ D = (4)² - 4×1×4
⇒ D = 16 - 16
⇒ D = 0
Thus, The discriminant of quadratic equation is,
⇒ D = 0
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