..............................
Answer:
[tex]x=17[/tex]
Step-by-step explanation:
[tex](6x+10)(x+17)(4x-34)[/tex]
[tex]6x+10+x+17+4x-34=180[/tex]
Add:- [tex]6x+x+4x=11x[/tex]
and [tex]10+17-34=-7[/tex]
So, [tex]11x-7=180[/tex]
Add 7 to both sides:-
[tex]11x=187[/tex]
Divide both sides by 11:-
[tex]\frac{11x}{11}=\frac{187}{11}[/tex]
[tex]x=17[/tex]
OAmalOHopeO
Find:P(large or blue)
Answer:
7/10
Step-by-step explanation:
Total number = 17+3+8+12 = 40
The ones that are large are 17 and 8
The ones that are blue are 17 and 3
Do not count the 17 twice
P(large or blue) = (17+3+8)/40
= 28/40
=7/10
The height of an object dropped from the top of a 144-foot building is given by ℎ(. How long will it take the object to hit the ground?)=―162+144
Answer:
Step-by-step explanation: h(t) = -16t2 + 144
h(1) = -16(12) + 144 = 128 ft
h(2) = -16(22) + 144 = 80 ft
h(2) - h(1) = 80 - 128 = -48 ft
It fell 48 ft between t = 1 and t = 2 seconds.
It reaches the ground when h(t) = 0
0 = -16t2 + 144
t = √(144/16) s = 3s
It reaches the ground 3s after being dropped.
2 men can build a wall in 10 days. in how many days will 8 men build the wall?
Step-by-step explanation:
8 men can do 60 man days of work by dividing 60 man days by the 8 men, which gives us 60/8 = 7 1/2 da
Find the probability that z lies between 0 and 1.56.
Answer:
P(0 < z < 1.56)=0.4406
Step-by-step explanation:
What is the dimension of the null space Null (A) of A =
Answer:
the nullity of a matrix A is the demision of its null space:nullity A = dim (n(A).
The average weekly assignment score of students in a statistics class is 7 out of 10 points. The professor proposes new incentives to boost the score of the students (like providing internship contacts etc.) He hopes that the results of running this incentives plan for a trial during the next couple of weeks will enable him to conclude that the incentives he offers increase the average weekly assignment score of students. What is the null hypothesis.
A. The average weekly score is strictly more than or equal to 7.
B. The average weekly score is less than our equal to 7.
C. The average weekly score is strictly less than 7.
D. The average weekly score is strictly more than 7.
Answer:
B. The average weekly score is less than or equal to 7.
Step-by-step explanation:
The average weekly assignment score of students in a statistics class is 7 out of 10 points. Test if it has increased.
This means that at the null hypothesis it is tested that the mean score of the students has not increased, that is, it still is of at most 7, so:
[tex]H_0: \mu \leq 7[/tex]
And thus, the correct answer is given by option b.
Maria is using a meter stick to determine the height of a door. If the smallest unit on the meter stick is centimeters, which measurement could Maria have used to most accurately record the height of the
door?
Answer:
2.31 m
Step-by-step explanation:
with marking down to centimeter length, one can only estimate accurately to the nearest centimeter or hundredth of a meter.
Answer:2.31 meter
Step-by-step explanation: none
Question 4 plz show ALL STEPS
Part (a)
Locate x = -1 on the x axis. Draw a vertical line through this x value until you reach the f(x) curve. Then move horizontally until you reach the y axis. You should arrive at y = 4. Check out the diagram below to see what I mean.
Since f(-1) = 4, this means we can then say
g( f(-1) ) = g( 4 ) = 4
To evaluate g(4), we'll follow the same idea as what we did with f(x). However, we'll start at x = 4 and draw a vertical line until we reach the g(x) curve this time.
Answer: 4==========================================================
Part (b)
We use the same idea as part (a)
f(-2) = 5
g( f(-2) ) = g(5) = 6
Answer: 6==========================================================
Part (c)
Same idea as the last two parts. We start on the inside and work toward the outside. Keep in mind that g(x) is now the inner function for this part and for part (d) as well.
g(1) = -2
f( g(1) ) = f(-2) = 5
Answer: 5==========================================================
Part (d)
Same idea as part (c)
g(2) = 0
f( g(2) ) = f( 0 ) = 3
Answer: 3I will mark as brainliest:)
Answer:
Point E.
.................
if a bicycle is 2.5 feet in diameter and races for 345 feet how many time does the wheel turn
A representative for a soup company conducted a survey
to determine whether people in a city were aware of the
soup company's new advertising campaign. The
researcher set up a booth outside a local supermarket for
7 days and asked randomly selected patrons as they
entered the store whether they would be willing to
participate in a survey. Of the 530 selected patrons,
482 agreed to take the survey, and 48 refused. Which of
the following factors makes it least likely that a reliable
conclusion can be drawn about the awareness of the soup
company's advertising campaign by all people in the
city?
A) Sample size
B) Population size
C) The number of days the survey was given
D) Where the survey was given
Answer:
Step-by-step explanation:
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Angelica’s bouquet of dozen roses contains 5 white roses. The rest of the roses. What fraction of the bouquet is pink? There are 12 roses in a dozen
Answer:
7/12
Step-by-step explanation:
total: 12 roses
white roses: 5
pink roses: 7
fraction of pink roses = 7/12
Jerod hopes to earn $1200 in interest in 4.9 years time from $24,000 that he has available to invest. To decide if it's feasible to do this by investing In an account that compounds monthly, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places
Answer:
The annual interest rate would have to be of 0.1%.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Jerod hopes to earn $1200 in interest in 4.9 years time from $24,000 that he has available to invest.
This means that:
[tex]A(4.9) = 1200 + 24000 = 25200[/tex]
[tex]t = 4.9[/tex]
[tex]P = 24000[/tex]
Compounded monthly:
This means that [tex]n = 12[/tex]
What would the annual rate of interest have to be?
We have to solve for r, so:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]25200 = 24000(1 + \frac{r}{12})^{12*4.9}[/tex]
[tex](1 + \frac{r}{12})^{12*4.9} = \frac{25200}{24000}[/tex]
[tex](1 + \frac{r}{12})^{58.8} = 1.05[/tex]
[tex]\sqrt[58.8]{(1 + \frac{r}{12})^{58.8}} = \sqrt[58.8]{1.05}[/tex]
[tex]1 + \frac{r}{12} = (1.05)^{\frac{1}{58.8}}[/tex]
[tex]1 + \frac{r}{12} = 1.00083[/tex]
[tex]\frac{r}{12} = 0.00083[/tex]
[tex]r = 12*0.00083[/tex]
[tex]r = 0.001 [/tex]
The annual interest rate would have to be of 0.1%.
Please Help!
What is the locus of the midpoints of all chords that can be drawn from a given point on a circle with a radius of 6.
The locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.
Given: A circle of radius 6 units
To find: The locus of the midpoint of all chords that can be drawn from a given point on the circle.
To find the required locus, we need to know the following:
Locus of a moving point is the trajectory of that point. It is the geometrical figure represented by the equation which is satisfied by the coordinates of the moving point.A chord of a circle is a line segment joining any points of a circle.Equation of a circle with center at origin and radius of [tex]r[/tex] units is [tex]x^{2} +y^{2} =r^{2}[/tex] According to the midpoint formula, the coordinates of the midpoint of the line segment joining the points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )[/tex]Let, without loss of generality, the given circle be centered at the origin. Even if it is not, we can shift the origin to the center of the given circle with coordinate transformation.
Then, the equation of the given circle is [tex]x^{2}+y^{2} =6^{2}[/tex], that is, [tex]x^{2}+y^{2} = 36[/tex]
Let the coordinates of the given fixed point be [tex](a,b)[/tex]
Let the coordinates of any point on the circle be [tex](p,q)[/tex] and let the coordinates of the midpoint of the chord joining the points [tex](a,b)[/tex] and [tex](p,q)[/tex] be [tex](h,k)[/tex]
We have to find the locus of [tex](h,k)[/tex]
Then, using the midpoint formula,
[tex](h,k)=(\frac{a+p}{2} ,\frac{b+q}{2})[/tex]
On solving, we get,
[tex]p=2h-a,q=2k-b[/tex]
Since [tex](a,b)[/tex] and [tex](p,q)[/tex] are both points on the given circle, they satisfy the equation of the circle, [tex]x^{2}+y^{2} = 36[/tex]
Then,
[tex]a^{2} +b^{2} =36[/tex]
[tex]p^{2} +q^{2} =36[/tex]
Substituting [tex]p=2h-a,q=2k-b[/tex] in [tex]p^{2} +q^{2} =36[/tex], we have,
[tex](2h-a)^{2} +(2k-b)^{2} =36[/tex]
[tex](2(h-\frac{a}{2}) )^{2} +(2(k-\frac{b}{2}))^{2} =36[/tex]
[tex]4(h-\frac{a}{2})^{2} +4(k-\frac{b}{2})^{2} =36[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =\frac{36}{4}[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =9[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =3^{2}[/tex]
This is the locus of the point [tex](h,k)[/tex]
Replace [tex](h,k)=(x,y)[/tex] to get,
[tex](x-\frac{a}{2})^{2} +(y-\frac{b}{2})^{2} =3^{2}[/tex]
This is the equation of a circle with center at [tex](\frac{a}{2} ,\frac{b}{2} )[/tex] and radius 3 units.
Thus, we can conclude that the locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.
Learn more about locus here:
https://brainly.com/question/23824483
I need the help ASAP please
Answer:
Option B
Answered by GAUTHMATH
Jack is 4 times as old as Lacy. 3 years from now the sum of their ages will be 71 . How old are they now?
Answer:
Lacy is 13 and Jack is 52
Step-by-step explanation:
In 3 years their ages will add up to 71 so you have to subtract 6 as there are two of them to get 65. Lacy's age is represented by x and since Jack is 4 times older his age is represented by 4x. So added together their age is 5x. So 5x=65. Then 65/5=13. So 13=x. So Lacy is 13 and Jack is 52 as 13x4 is 52.
In a model, a submarine is located at point (0, 0) on the coordinate plane. The submarine’s radar range has an equation of 2x2 + 2y2 = 128
Draw the figure on a graph and label the location of the submarine. Make sure your name is on the paper, and label this activity Part 2.
Can the submarine’s radar detect a ship located at the point (6, 6) ? Mark that location on your graph, and explain how you know whether or not the ship will be detected in the space provided on the Circles Portfolio Worksheet.
Answer:
Remember that for a circle centered in the point (a, b) and with a radius R, the equation is:
(x - a)^2 + (y - b)^2 = R^2
Here we know that the submarine is located at the point (0, 0)
And the radar range has the equation:
2*x^2 + 2*y^2 = 128
You can see that this seems like a circle equation.
If we divide both sides by 2, we get:
x^2 + y^2 = 128/2
x^2 + y^2 = 64 = 8^2
This is the equation for a circle centered in the point (0, 0) (which is the position of the submarine) of radius R = 8 units.
The graph can be seen below, this is just a circle of radius 8.
We also want to see if the submarine's radar can detect a ship located in the point (6, 6)
In the graph, this point is graphed, and you can see that it is outside the circle.
This means that it is outside the range of the radar, thus the radar can not detect the ship.
Find the area of the shape shown below.
Answer:
28 units²
Step-by-step explanation:
Area of trapezoid =
2(8 + 4)/2 = 12
Area of rectangle =
2 x 8 = 16
16 + 12 = 28
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
There is 3m wide path around a circular cricket ground having the diameter of 137 m. Find the area of the path.
Answer:
1320 m^2
Step-by-step explanation:
area of ground = π r ^2
= (22/7) × (137/2)^2
= 14,747.0714286 m^2
area of ground and path
=( 22/7)(143/2)^2
= 16,067.0714286 m^2
area of path
=16,067.0714286 -14,747.0714286
= 1320 m^2
note :
r = radius = diameter /2
area of a circle = π r^2
diameter of circle created with path and ground = 137 + 2 × width of path
= 137 + 2× 3 = 143 m
A particular variety of watermelon weighs on average 22.4 pounds with a standard deviation of 1.36 pounds. Consider the sample mean weight of 64 watermelons of this variety. Assume the individual watermelon weights are independent.
Required:
a. What is the expected value of the sample mean weight?
b. What is the standard deviation of the sample mean weight?
c. What is the approximate probability the sample mean weight will be less than 22.02?
d. What is the value c such that the approximate probability the sample mean will be less than c is 0.9?
Answer:
a) 22.4 pounds.
b) 0.17 pounds.
c) 0.0127 = 1.27% approximate probability the sample mean weight will be less than 22.02.
d) c = 22.62
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
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.
Average 22.4 pounds with a standard deviation of 1.36 pounds.
This means that [tex]\mu = 22.4, \sigma = 1.36[/tex]
Consider the sample mean weight of 64 watermelons of this variety.
This means that [tex]n = 64, s = \frac{1.36}{\sqrt{64}} = 0.17[/tex]
a. What is the expected value of the sample mean weight?
By the Central Limit Theorem, 22.4 pounds.
b. What is the standard deviation of the sample mean weight?
By the Central Limit Theorem, 0.17 pounds.
c. What is the approximate probability the sample mean weight will be less than 22.02?
This is the p-value of Z when X = 22.02. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{22.02 - 22.4}{0.17}[/tex]
[tex]Z = -2.235[/tex]
[tex]Z = -2.235[/tex] has a p-value of 0.0127.
0.0127 = 1.27% approximate probability the sample mean weight will be less than 22.02.
d. What is the value c such that the approximate probability the sample mean will be less than c is 0.9?
This is the 90th percentile, that is, [tex]X = c[/tex] when z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.28 = \frac{c - 22.4}{0.17}[/tex]
[tex]c - 22.4 = 1.28*0.17[/tex]
[tex]c = 22.62[/tex]
what is the area of the triangle ://
Answer:
The area of a triangle is:
Area = 1/2(bh)
Area = 1/2(70)
Area = 35 square inches
Let me know if this helps!
Question 12 plz show ALL STEPS
9514 1404 393
Answer:
θ = 1.5 radians ≈ 85.9°
Step-by-step explanation:
The arc length in terms of central angle and radius is ...
s = rθ
where θ is the central angle in radians. Here, we want to find θ, so we have ...
θ = s/r . . . . divide by r
For the given numbers, ...
θ = (6 cm)/(4 cm) = 3/2 = 1.5 . . . radians
I radian is 180°/π, so 3/2 radians is ...
(3/2)(180°/π) = 270°/π ≈ 85.9°
WILL GIVE BRAINLIST IF CORRECT Which function is represented by this graph
Answer:
Step-by-step explanation:
B; So this is a transformation problem from the parent function of f(x)=|x| so the function is is moved 3 units down giving it the -3 at the end and is moved to the right 7 units so it would be x-7
Can someone explain this to me please
Answer: Choice B
Explanation:
Everywhere you see an x, replace it with a+2.
[tex]f(x) = 3(x+5)+\frac{4}{x}\\\\f(a+2) = 3(a+2+5)+\frac{4}{a+2}\\\\f(a+2) = 3(a+7)+\frac{4}{a+2}\\\\[/tex]
the length of a rectangle is 4 meters longer than the width. if the area is 22 square meters , find the rectangle dimension
Let breadth be x
Length=x+4We know
[tex]\boxed{\sf Area_{(Rectangle)}=Length\times Breadth}[/tex]
[tex]\\ \sf\longmapsto x(x+4)=22[/tex]
[tex]\\ \sf\longmapsto x^2+4x=22[/tex]
[tex]\\ \sf\longmapsto x^2+4x-22=0[/tex]
By solving[tex]\\ \sf\longmapsto x=-2\pm\sqrt{26}[/tex]
It doesnot have any real roots
Triangle DEF contains right angle E. If angle D measures 40° and its adjacent side measures 7.6 units, what is the measure of side EF? Round your answer to the nearest hundredth.
[tex]\\ \rm\longmapsto cot40=\dfrac{7.6}{EF}[/tex]
[tex]\\ \rm\longmapsto EF=\dfrac{7.6}{cot40}[/tex]
[tex]\\ \rm\longmapsto EF=\dfrac{7.6}{1.19}[/tex]
[tex]\\ \rm\longmapsto EF=6.38units[/tex]
Answer:
[tex]\displaystyle 6,38\:units[/tex]
Step-by-step explanation:
You would set your proportion up like so:
[tex]\displaystyle \frac{7,6}{EF} = cot\:40° \\ \\ 7,6 = EFcot\:40° → 6,3771571969... = \frac{7,6}{cot\:40°} \\ \\ 6,38 ≈ EF[/tex]
I am joyous to assist you at any time.
Coefficient and degree of the polynomial
Answer:
The leading coefficient is -8 as it is a mix of x and cardinal, if it was x alone then it wouldn't be the coefficient, we would use the next number shown.
If it was just a number and no x then it would still be the coefficient.
The degree is 9 as it is the highest power shown.
Step-by-step explanation:
See attachment for examples
In the diagram, the perimeter of the rectangle is 56. What is its area?
What is the equation
Answer:
y=3x+1
Step-by-step explanation:
Determine slope with two coordinates and use it in the formula
