Answer:
Yes, it will overflow after 16 minutes..
Step-by-step explanation:
The tub fills at a rate of 5 gallons every minute, but it drains at a rate of 2.5 gallons every minute. This means that it fills twice as fast as it drains, so it would take 16 minutes for the tub to overflow. If you subtract the rate of draining from the rate of filling then the net rate of water going up is 2.5 gallons a minute.
PLS HELP
Choose the inequality that represents the following graph,
+
-4
-5
-3
- 2
-1
0
1
2
3
4
5
Choose 1 answers
ISO
IO
D
>O
Answer:
The option which represents the inequality is option D ; stated as x ≥ 0
Step-by-step explanation:
The marked or dotted position is 0 ; which represents the position of x, when graphing inequality statements, if the point IS SHADED, then it means GREATER THAN EQUAL TO.
Option A is incorrect, the inequality sign is not the same as the direction of the arrow.
Option B, says LESS THAN EQUAL TO, instead of GREATER THAN EQUAL TO
Option C SAYS GREATER THAN instead of GREATER THAN EQUAL TO.
Therefore, Option D is the correct expression which means x is GREATER THAN EQUAL TO.
Learn more : https://brainly.com/question/24065770
Find the number in which 9 has greater value.
0.5689
5.6890
56.89
569.80
Answer:
569.80Step-by-step explanation:
Among all the choices, the digit 9 has the greatest value in number 569.80. For the reason that 9 got ones value - which are greatest than other.[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Solve for 2. Round to the nearest tenth, if necessary.
L
58
M
Answer: 2=
Submit Answer
attempt 1 out of 2
PLS HELP
Answer:
x = 46.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 54 = x / 58
58 sin 54 =x
x=46.92298
To the nearest tenth
x = 46.9
slove for inequality of -6> t-(-13)
Step-by-step explanation:
-6>t-(-13)
= -6>t+13
= -6-13>t
= -19>t
= t<-19
Answer:
t < - 19
Step-by-step explanation:
Given
- 6 > t - (- 13) , that is
- 6 > t + 13 ( subtract 13 from both sides )
- 19 > t , then
t < - 19
Find the square root of 1764 by factorisation method
Answer:
42
Step-by-step explanation:
prime factorisation of 1764 = 2^2 × 3^2 × 7^2
hence,
√1764 = √(2^2 × 3^2 × 7^2) =2 x 3 x 7 = 42
Answer:
42
Step-by-step explanation:
1764 = 2 * 882
= 2 * 2 * 441
= 2 * 2 * 3 * 147
= 2 * 2 * 3 * 3 * 49
= 2 * 2 * 3 * 3 * 7 * 7
[tex]\sqrt{1764} = \sqrt{2*2*3*3*7*7} = 2*3*7 = 42[/tex]
Use the diagram (click the image above) to find the measure of the segment or angle.
1. m
2. m
3. GH =
4. BC =
Answer:
Step-by-step explanation:
From the given angles ∠ABC and ∠GHK,
m∠ABC = m∠GHK [Given]
m∠ABC = m∠GHL + m∠KHL [Since, ∠GHL + ∠KHL = ∠GHK]
(6x + 2)° = (5x - 27)° + (3x + 1)°
6x + 2 = 8x - 26
8x - 6x = 28
2x = 28
x = 14
m(BC) = m(HK) [Given]
3z + 6 = 8z - 9
8z - 3z = 6 + 9
5z = 15
z = 3
m(AB) = m(GH)
5y - 8 = 3y
2y = 8
y = 4
m∠ABC = mGHK = (6x + 2)
= 6(14) + 2
= 86°
m(AB) = m(GH) = 3y
= 3(4)
= 12 units
m(BC) = m(HK) = (3z + 6)
= 3(3) + 6
= 15 units
m(∠KHL) = (3x + 1)°
= 3(14) + 1
= 43°
Rectangle KLMN has vertices K(-5,6), L(-2,9), M(6, 1), and N(3,-2). Determine and state the coordinates of the point of intersection of the diagonals.
Answer:
(0.5,3.5)
Step-by-step explanation:
First, we can draw the image, as shown. The diagonals in the rectangle are the following lines:
from (-2,9) to (3,-2)
from (-5, 6) to (6,1)
To find where they intersect, we can start by making an equation for the lines. For an equation y=mx+b, m represents the slope and b represents the y intercept, or when x=0
For the first line, from (-2,9) to (3,-2), we can calculate the slope by calculating the change in y/change in x = (y₂-y₁)/(x₂-x₁). If (3,-2) is (x₂,y₂) and (-2,9) is (x₁,y₁), our slope is
(-2-9)/(3-(-2)) = -11/5
Therefore, our equation is
y= (-11/5)x + b
To solve for b, we can plug a point in, like (3,-2). Therefore,
-2=(-11/5)*3+b
-2=-33/5+b
-10/5=-33/5+b
add 33/5 to both sides to isolate b
23/5=b
Our equation for one diagonal is therefore y=(-11/5)x+23/5
For the second line, from (-5, 6) to (6,1), if (6,1) is (x₁,y₁) and (-5,6) is (x₂,y₂), the slope is (1-6)/(6-(-5)) = -5/11 . Plugging (6,1) into the equation y=(-5/11)x+b, we have
1=(-5/11)*6+b
11/11 = -30/11 + b
add 30/11 to both sides to isolate b
41/11 = b
our equation is
y = (-5/11) x + 41/11
Our two equations are thus
y = (-5/11) x + 41/11
y=(-11/5)x+23/5
To find where they intersect, we can set them equal to each other
(-11/5)x+23/5 = y = (-5/11) x + 41/11
(-11/5)x + 23/5 = (-5/11)x + 41/11
subtract 23/5 from both sides as well as add 5/11 to both sides to make one side have only x values and their coefficients
(-11/5)x + (5/11)x = 41/11-23/5
11*5 = 55, so 55 is one value we can use to make the denominators equal.
(-11*11/5*11)x+(5*5/11*5)x=(41*5/11*5)-(23*11/5*11)
(-121/55)x+(25/55)x = (205/55) - (253/55)
(-96/55)x = (-48/55)
multiply both sides by 55 to remove the denominators
-96x=-48
divide both sides by -96 to isolate x
x=-48/-96=0.5
plug x=0.5 into a diagonal to see the y value of the intersection
(-11/5)x + 23/5 = y = (-11/5)* 0.5 + 23/5 = 3.5
Which term of the AP. 8 , -4 , -16 , -28 ,......... is -880 ?
Answer: 75th term
Step-by-step explanation:
If you look at the first terms, you can see that we're subtracting 12 from the previous term to get the number. Knowing this, we can write an expression for the nth term. The expression would be -12n + 20. Since this specific term has value of -880, we set -880 equal to the value of -12n+20. By setting your equation like this -12n + 20 = -880 and solving, you get n = 75, which means the 75th term has a value of -880.
help me with this two I don't understand
Step-by-step explanation:
5.
[tex](5 + 4 \sqrt{7} ){x}^{2} + (4 - 2 \sqrt{7} ) x- 1 = 0[/tex]
Simplify both radicals.
[tex](5 + \sqrt{112) {x}^{2} } + (4 - \sqrt{28} )x - 1 = 0[/tex]
Apply Quadratic Formula
First. find the discramnint.
[tex](4 - \sqrt{28} ) {}^{2} - 4(5 + \sqrt{112} )( - 1) = 64[/tex]
Now find the divisor 2a.
[tex]2(5 + \sqrt{112} ) = 10 + 8 \sqrt{7} [/tex]
Then,take the square root of the discrimant.
[tex] \sqrt{64} = 8[/tex]
Finally, add -b.
[tex] - (4 + 2 \sqrt{7} )[/tex]
So our possible root is
[tex] - (4 + 2 \sqrt{7} ) + \frac{8}{10 + 8 \sqrt{7} } [/tex]
Which simplified gives us
[tex] \frac{ 4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } [/tex]
Rationalize the denominator.
[tex] \frac{4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } \times \frac{10 - 8 \sqrt{7} }{10 - 8 \sqrt{7} } = \frac{ - 72 - 12 \sqrt{7} }{ - 348} [/tex]
Which simplified gives us
[tex] \frac{6 + \sqrt{7} }{29} [/tex].
6. The answer is 2.
9514 1404 393
Answer:
5. x = (6 +√7)/29; a=6, b=1, c=29
6. x = 2
Step-by-step explanation:
5.The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.
[tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-(4-2\sqrt{7})+\sqrt{(4-2\sqrt{7})^2-4(5+4\sqrt{7}})(-1)}{2(5+4\sqrt{7})}\\\\=\dfrac{-4+2\sqrt{7}+\sqrt{16-16\sqrt{7}+28+20+16\sqrt{7}}}{10+8\sqrt{7}}=\dfrac{4+2\sqrt{7}}{2(5+4\sqrt{7})}\\\\=\dfrac{(2+\sqrt{7})(5-4\sqrt{7})}{(5+4\sqrt{7})(5-4\sqrt{7})}=\dfrac{10-3\sqrt{7}-28}{25-112}=\boxed{\dfrac{6+\sqrt{7}}{29}}[/tex]
__
6.Use the substitution z=3^x to put the equation in the form ...
z² -3z -54 = 0
(z -9)(z +6) = 0 . . . . . factor
z = 9 or -6 . . . . . . . . value of z that make the factors zero
Only the positive solution is useful, since 3^x cannot be negative.
z = 9 = 3^2 = 3^x . . . . use the value of z to find x
x = 2
Find the value of each variable.
The two congruent base angles tell us that this triangle is isosceles, meaning it has two congruent sides. Therefore, we can set the two expressions equal to each other and solve from there.
9x - 73 = 3x + 23
6x - 73 = 23
6x = 96
x = 16
Side = 3(16) + 23 = 48 + 23 = 71
Hope this helps!
Answer:
x = 16
Step-by-step explanation:
Since the base angles are the same, the side lengths are the same
9x- 73 = 3x+23
Subtract 3x from each side
9x - 3x- 73 = 3x+23 -3x
6x- 73 = 23
Add 73 to each side
6x - 73 +73 = 23+73
6x = 96
Divide by 6
6x/6 = 96/6
x =16
A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre of the pasture at any given time, so he has some images of the pasture taken by the state department of agriculture’s aerial photography division. Here are three samples of the images.
Sample 1 : 4
Sample 2 : 1
Sample 3 : 9
What margin of error is reasonable for these samples?
Answer:
Sample 1 MOE = 37.24%
Sample 2 MOE = 29.4%
Sample 3 MOE = None
Step-by-step explanation:
We are told that 250 sheep grazes over a 40-acre pasture.
Thus, number of sheeps per acre = 250/40 = 6.25 ≈ 6
Thus, n = 6
For the samples given, we can find sample proportions as;
Sample 1: p_o = 4/6 = 0.67
Sample 2: p_o = 1/6 = 0.17
Sample 3: p_o = 9/6 = 1.5
Formula for test statistic here is;
z = √(p_o(1 - p_o)/n)
For sample 1;
z = √(0.67(1 - 0.67)/6)
z ≈ 0.19
For sample 2;
z = √(0.17(1 - 0.17)/6)
z ≈ 0.15
For sample 3;
z = √(1.5(1 - 1.5)/6)
z = √−0.125
We are not given confidence level but we will use 95%.
Value of z_α at 95% Confidence level is 1.96. Thus, we can find the margin of error for the samples;
For sample 1;
Margin of error at z = 0.19 is;
1.96 × 0.19 = 0.3724 = 37.24%
For sample 2;
Margin of error at z = 0.15 is;
1.96 × 0.15 = 0.294 = 29.4%
For sample 3;
Since test statistic has a negative square root, then it has no margin of error.
Please write down your work on the loose leaf, take a CLEAR picture, and upload here. Thank you.
Answer:
m(∠C) = 18°
Step-by-step explanation:
From the picture attached,
m(arc BD) = 20°
m(arc DE) = 104°
Measure of the angle between secant and the tangent drawn from a point outside the circle is half the difference of the measures of intercepted arcs.
m(∠C) = [tex]\frac{1}{2}[\text{arc(EA)}-\text{arc(BD)}][/tex]
Since, AB is a diameter,
m(arc BD) + m(arc DE) + m(arc EA) = 180°
20° + 104° + m(arc EA) = 180°
124° + m(arc EA) = 180°
m(arc EA) = 56°
Therefore, m(∠C) = [tex]\frac{1}{2}(56^{\circ}-20^{\circ})[/tex]
m(∠C) = 18°
The battery standby duration (in hours) of a new model of cell phone is known to be normally distributed. Ten pieces of such new model of cell phone supplied from the manufacturer are randomly chosen and the actual standby durations are recorded as below:
48.2 47.8 45.6 47.2 49.3
51.2 44.2 45.4 49.2 43.6
(a) Calculate the unbiased estimates of population mean and standard deviation of battery standby duration (in hours) of the new cell phone.
(b) The manufacturer claimed that this new model of cell phone has the mean battery standby duration of longer than 46.5 hours. Test at 1% significance level if this claim is true.
x = number of hours
want to find probability (P) x >= 13
x is N(14,1) transform to N(0,1) using z = (x - mean) / standard deviation so can look up probability using standard normal probability table.
P(x >= 13) = P( z > (13 - 14)/1) = P(z > -1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413
To convert that to percentage, multiply 100, to get 84.13%
Which is the graph of f(x) = (2)* ?
Answer:
the graph of f(x)=×2 called a parabola
[tex]\sqrt\\x^{2} - 3\\[/tex]
helppppppppppppppppppp helppppppppppppp
HOPE ITS HELPFUL ^_^
•RHONAGiven that squareroot 9.8 = 3.13 and squareroot 98 = 9.9 , then squareroot 98000=??
How they connected?
Answer:
see your answer in pic
mark me brainlist
Step-by-step explanation:
A traveling salesman figures it costs 28
cents for every mile he drives his car. How much does it cost him (in dollars) a week to drive his car if he travels 315 miles a week?
Using the proportion you found in Question 3, write an equation for the length of arc EF in terms of the radii of AB and AC and the length of arc CD.
Answer:
Step-by-step explanation:
tìm điều kiện xác định để phân thức A=(1/x-2-2x/4-x^2+1/2+x).(2/x-1)
Find x if AC = 7x - 15 and BD = 4x + 15
Answer:
x = 10
Step-by-step explanation:
7x - 15 = 4x + 15
7x - 4x = 15 + 15
3x = 30
x = 10
Answer:
x = 10
Step-by-step explanation:
Given that AC and BD are congruent , then
7x - 15 = 4x + 15 ( subtract 4x from both sides )
3x - 15 = 15 ( add 15 to both sides )
3x = 30 ( divide both sides by 3 )
x = 10
What is the approximate length of the line segment?
(1, -1)
(6,-8)
Answer:
8.6023
Step-by-step explanation:
length = √[(x2-x1)^2+(y2-y1)^2]
=√[(1-6)^2+(-1--8)^2] =√74 =8.6023
What is the equation of the graph
Answer:
[tex]y = 2x^2 + 1[/tex]
Step-by-step explanation:
The graph you see there is called a parabola. The general equation for the graph is as below
[tex]y = a*x^2 + b[/tex]
To find the equation we need to find the constants a and b. The constant b is just how much we're lifting the parabola by. Notice it's lifted by 1 on the y axis.
To find a it's a little more tricky. Let's use the graph to find a value for a by plugging in values we know. We know that b is 1 from the previous step, and we know that when x=1, y=3. Let's use that!
[tex]3 = a * (1)^2 + 1\\2 = a[/tex]
Awesome, we've found both values. And we can write the result.
[tex]y = 2x^2 + 1[/tex]
I'll include a plotted graph with our equation just so you can verify it is indeed the same.
Can somebody help me please!!!!!
Answer:
0
Step-by-step explanation:
g[f(x)] = x^2 - 3
= 3x^2
if gf(0) = 3(0)^2
= 0
Graph the function need ASAP help
Is it a, b , c or d?
Answer:
D
Step-by-step explanation:
(the line is a / shape, so the slope is positive)
(the line crosses the y axis at (0,-2)
(using the above information, the equation is y=2x-2)
Answer:
y = 2x - 2
Step-by-step explanation:
Start with
y = mx + b
The graph shows the y-intercept -2.
We have y = mx - 2
slope = m = rise/run
The slope is rise of 2 and run of 1, so m = 2.
y = 2x - 2
In a large midwestern university (the class of entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 2001 an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. The proportion of all entering freshmen in 1999 and 2001, who graduated in the bottom third of their high school class, are p1 and p2, respectively.Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared to the proportion in 1999? To determine this, you test the hypothesesH0 : p1 = p2 , Ha : p1 > p2.The P-value of your test isA. 0.976.B. 0.024.C. 0.048.D. 0.001.
Answer:
B. 0.024
The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
1999:
Of 100, 20 were in the bottom thid. So
[tex]p_B = \frac{20}{100} = 0.2[/tex]
[tex]s_B = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
2001:
Of 100, 10 were in the bottom third, so:
[tex]p_A = \frac{10}{100} = 0.1[/tex]
[tex]s_A = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
To determine this, you test the hypotheses H0 : p1 = p2 , Ha : p1 > p2.
Can also be rewritten as:
[tex]H_0: p_B - p_A = 0[/tex]
[tex]H_1: p_B - p_A > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the sample:
[tex]X = p_B - p_A = 0.2 - 0.1 = 0.1[/tex]
[tex]s_A = \sqrt{s_A^2+s_B^2} = \sqrt{0.03^2+0.04^2} = 0.05[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.1 - 0}{0.05}[/tex]
[tex]z = 2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference of proportions of at least 0.1, which is 1 subtracted by the p-value of z = 2.
Looking at the z-table, z = 2 has a p-value of 0.976.
1 - 0.976 = 0.024, so the p-value is given by option B.
The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Miguel withdrew $20 per week from his bank account for 4 weeks. Which expression shows the charge in his account balance?
a. -20 + 4
b. -20 - 4
c. -20 • 4
d. -20 / 4
(I think it’s C)
Please help me, this is due for tomorrow!
Answer:
C
Step-by-step explanation:
You are correct
*Per something means multiplication*
20 per 4 weeks = 20 × 4
PLS HELP ME
The width of a rectangle is 20m to 2 significant figures
The length of a rectangle is 40m to 1 significant figure
What is the shortest perimeter the rectangle could have?
Answer:
80m
Step-by-step explanation:
(20x2) =40m + 40m= 80m
What does the greater unit rate or slope mean in terms of the situation? What can you conclude from this?
Answer:
Bruce's tiles covered more area than Felicia's, so this means Bruce has the greater unit rate.
Step-by-step explanation:
Got it right
Find the equation of a line perpendicular to y = (75)x - 1 and has a y-
intercept of 1.
Answer:
6y = -5x + 6
y = -5/6 x + 1
Step-by-step explanation:
y = -5/6 x + b
1 = b
