Answer:
2/3
Step-by-step explanation:
We can find the slope by using the slope formula
m= (y2-y1)/(x2-x1)
= (-4-2)/(-1-8)
= -6/ -9
= 2/3
Which is the best estimate of 90/7 divided by 1 3/4
Answer:
90/4= 12.9
1*3/4= 0.75
Step-by-step explanation:
solve the equation 4x +30 = 2(x-10)
M5-3/2x less than or equal to 1/3
Answer: choice A
Step-by-step explanation:
by rearranging the initial inequality you’ll get
[tex]\frac{3}{2} x\leq 5-\frac{1}{3}[/tex]
which equals
[tex]\frac{3}{2} x\leq\frac{14}{3}[/tex]
then multiply both sides by 2/3
[tex]x\leq \frac{28}{9}[/tex]
x=(y+2)^2 solve the equation
Answer:
x= y^2+4y+4
Step-by-step explanation:
x= (y+2)(y+2)
x= y^2+2y+2y+4
x= y^2+4y+4
Answer:
X = y^2 + 4y + 4
Y= (√X) -2
Step-by-step explanation:
X = (Y+2)^2
X = (Y+2)(Y+2)
X = Y^2 + 4y + 4
X = (Y+2)^2
√X = √(Y+2)^2 (taking the root of both sides cancels the exponent)
√X = Y+2
-2 -2
(√X) - 2 = Y
or
Y = (√X) - 2
Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2, ... are not vectors but are entries in vectors. T(X1,X2,X3,X4) = (x1 +4x2, 0, 3x2 +x4, x2 -x4)
The transformation matrix for the mapping T is the matrix T such that
[tex]\mathbf T(\vec x)=T\,\vec x[/tex]
where
[tex]T=\begin{bmatrix}1&4&0&0\\0&0&0&0\\0&3&0&1\\0&1&0&-1\end{bmatrix}[/tex]
The correct matrix A is
[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]
To find the matrix A that represents the linear transformation T, we need to determine the coefficients that map the input vector (X₁, X₂, X₃, X₄) to the output vector (x₁ +4x₂, 0, 3x₂ +x₄, x₂ -x₄)
By comparing the corresponding entries in the input and output vectors, we can determine the coefficients of the matrix A.
The first row of A will have the coefficients for X₁ and X₂, which are 1 and 4 respectively. The second row will have all zeros since the output vector has a zero in the second position. The third row will have the coefficient 3 for X₂ and 1 for X₄. Finally, the fourth row will have the coefficient 1 for X₂ and -1 for X₄.
Thus, the matrix A that implements the mapping T is:
[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]
Learn more about linear transformation here:
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#SPJ2
Find the area of a circle with diameter, D = 8.1m.
Give your answer rounded to 1 DP (One decimal point)
The photo is attatched below
Answer:
51.5m
Step-by-step explanation:
half 8.1 to get the radius (4.05)
then times pi by 4.05 squared
your answer is 51.5 (rounded)
Which pairs of non-overlapping angles share a ray to make a right angle?
Answer:
JGH and JGF
Step-by-step explanation:
Both adjacent and make a right angle
∠KGJ and ∠FGH are the pairs of non-overlapping angles that share a ray to make a right angle.
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
In the given figure, we need to find the pairs of non-overlapping angles that share a ray to make a right angle.
We can see that ∠EGF and ∠HGF make a right angle but line FG is overlapping or common in both the angles.
∠KGJ and ∠FGH make a right angle and pairs of non-overlapping angles.
So, this is the correct pair for the condition.
Learn more about a right angle;
https://brainly.com/question/7116550
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
Central angle = 360-52=308°
In radians
308° = 308π/180
Now
S = r∅
S = 3×308π/180
S = 924π /180
S = 77π/15 in.
Answer:
answer is 13π/15
Step-by-step explanation:
correct answer is 13π/15.
8+8?
Pls help will mark you or whatever
Answer:
8+8=16
Step-by-step explanation:
Lets say you have 8 apples and your friend gives you 8 more apples. So, you count 9,10,11,12,13,14,15,16 which was 8 times.
Hope this helps.
A science club has 16 members. How many ways can a president, a Vice President, and a treasurer be selected from the members?
Answer:
3,360
Step-by-step explanation:
We calculate the number of permutations for this problem where the order in which we accommodate people matters to us as follows:
[tex]P=\frac{n!}{(n-r)!}[/tex]
where n is the total number of options we have; the total number of members: [tex]n=16[/tex]
and r is the number of places or positions we are considering which in this case are the President position, the Vice president position and the treasurer position ⇒ 3 positions in total ⇒ [tex]r=3[/tex]
substituting n and r in the formula:
[tex]P=\frac{16!}{(16-3)!} \\\\P=\frac{16!}{13!} \\\\P=3,360[/tex]
A president, a Vice President, and a treasurer can be selected from the members in 3,360 ways
Which expression is equivalent to (2g^3+4)^2
[tex]answer \\ 4g ^{6} + 16 \\ solution \\ ( {2g}^{3} + 4)^{2} \\ = 2 \times 2 \: g ^{3 \times 2} + 4 \times 4 \\ = 4 {g}^{6} + 16 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
4g^6+16 IS equivalent to (2g^3+4)^2
8. Mr. Azu invested an amount at rate of 12% per annum and invested another amount. GHe
580.00 more than the first at 14%. IN Mr. Azu had total accumulated amount of
GH42.358.60. how much was his total investment?
Ans:
Answer:
GH¢.37480.36
Step-by-step explanation:
Let the amount invested at 12% per annum =GH¢.x
He invested 580.00 more than the first at 14%.
Therefore:
The amount invested at 14% =GH¢.(x+580)
For each investment option:
Amount Accrued =Principal + Simple Interest
Amount Accrued at 12%
[tex]=x+x*0.12\\=1.12x[/tex]
Amount Accrued at 14%
[tex]=(x+580)+0.14(x+580)\\=x+580+0.14x+81.2\\=1.14x+661.2[/tex]
Mr. Azu had total accumulated amount of GH42,358.60
Therefore:
1.12x+1.14x+661.2=42,358.60
2.26x=42,358.60-661.2
2.26x=41697.4
x=GH¢.18450.18
Therefore:
The amount invested at 12% per annum= GH¢.18450.18
The amount invested at 14% per annum= GH¢.18450.18+580
=GH¢.19030.18
Mr Azu's Total Investment = 18450.18 +19030.18
=GH¢.37480.36
Q 4.19: To verify whether there are negative consequences of taking a new type of medicine, 3000 tests were conducted. Assume that the null hypothesis is that the new medicine has no negative effects and the alternative hypothesis is that the new medicine is potentially harmful. 31 of these tests gave significant results at a 1% significance level. What can we say about the potential harmfulness of the new medicine
Answer:
The p-value obtained is less than the significance level at which the test was performed at, hence, we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the the new medicine is potentially harmful.
Step-by-step explanation:
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, the null hypothesis is that the new medicine has no negative effects and the alternative hypothesis is that the new medicine is potentially harmful
Mathematically,
The null hypothesis is represented as
H₀: p = 0
The alternative hypothesis is represented as
Hₐ: p > 0
To do this test, we will use the z-distribution because although no information on the population standard deviation is known, the sample size is large enough.
So, we compute the test statistic
z = (x - μ)/σₓ
x = sample proportion = (31/3000) = 0.0103
μ = p₀ = 0
σₓ = standard error = √[p(1-p)/n]
where n = Sample size = 3000
σₓ = √[0.0103×0.9897/3000] = 0.0018462936 = 0.0018463
z = (0.0103 - 0) ÷ 0.0018463
z = 5.60
checking the tables for the p-value of this test statistic
Significance level = 1% = 0.01
The hypothesis test uses a one-tailed condition because we're testing only in one direction.
p-value (for z = 5.60, at 0.01 significance level, with a one tailed condition) = < 0.00001
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.01
p-value = < 0.00001
p-value < 0.00001 < 0.10
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the the new medicine is potentially harmful.
Hope this Helps!!!
Given: AB || DE , AD bisects BE.
Prove: ABC = DEC using the ASA postulate.
Answer:
As per ASA postulate, the two triangles are congruent.
Step-by-step explanation:
We are given two triangles:
[tex]\triangle ABC[/tex] and [tex]\triangle DEC[/tex].
AD bisects BE.
AB || DE.
Let us have a look at two properties.
1. When two lines are parallel and a line intersects both of them, then alternate angles are equal.
i.e. AB || ED and [tex]\angle B[/tex] and [tex]\angle E[/tex] are alternate angles [tex]\Rightarrow[/tex] [tex]\angle B = \angle E[/tex].
2. When two lines are cutting each other, angles formed at the crossing of two, are known as Vertically opposite angles and they are are equal.
[tex]\Rightarrow \angle ACB = \angle DCE[/tex]
Also, it is given that AD bisects BE.
i.e. EC = CB
1. [tex]\angle B = \angle E[/tex]
2. EC = CB
3. [tex]\angle ACB = \angle DCE[/tex]
So, we can in see that in [tex]\triangle ABC[/tex] and [tex]\triangle DEC[/tex], two angles are equal and side between them is also equal to each other.
Hence, proved that [tex]\triangle ABC[/tex] [tex]\cong[/tex] [tex]\triangle DEC[/tex].
Identify the type of sampling that is used: A list of all registered voters in a state is given to a researcher who would like to determine if a particular candidate is likely to be elected. The researcher has a computer randomly generate several hundred numbers, and those numbers are used to select names from the list to form a sample. a. systematic b. random c. convenience d. stratified
Answer:
The correct option is (b) random.
Step-by-step explanation:
A simple random sample is a part of a statistical population in which every individual of the population has an equal probability of being selected.
Assigning each individual of the population a unique number and using a computer or random number generator for selection is a procedure to select a simple random sample.
In this case the researcher has a computer randomly generate several hundred numbers, and those numbers are used to select names from the list to form a sample.
The procedure indicates that the researcher used a simple random sampling technique to select the sample.
Thus, the correct option is (b).
The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x.
Answer:
The correct option is (d).
Step-by-step explanation:
The complete question is:
The random variable x represents the number of computers that families have along with the corresponding probabilities. Use the probability distribution table below to find the mean and standard deviation for the random variable x.
x : 0 1 2 3 4
p (x) : 0.49 0.05 0.32 0.07 0.07
(a) The mean is 1.39 The standard deviation is 0.80
(b) The mean is 1.39 The standard deviation is 0.64
(c)The mean is 1.18 The standard deviation is 0.64
(d) The mean is 1.18 The standard deviation is 1.30
Solution:
The formula to compute the mean is:
[tex]\text{Mean}=\sum x\cdot p(x)[/tex]
Compute the mean as follows:
[tex]\text{Mean}=\sum x\cdot p(x)[/tex]
[tex]=(0\times 0.49)+(1\times 0.05)+(2\times 0.32)+(3\times 0.07)+(4\times 0.07)\\\\=0+0.05+0.64+0.21+0.28\\\\=1.18[/tex]
The mean of the random variable x is 1.18.
The formula to compute variance is:
[tex]\text{Variance}=E(X^{2})-[E(X)]^{2}[/tex]
Compute the value of E (X²) as follows:
[tex]E(X^{2})=\sum x^{2}\cdot p(x)[/tex]
[tex]=(0^{2}\times 0.49)+(1^{2}\times 0.05)+(2^{2}\times 0.32)+(3^{2}\times 0.07)+(4^{2}\times 0.07)\\\\=0+0.05+1.28+0.63+1.12\\\\=3.08[/tex]
Compute the variance as follows:
[tex]\text{Variance}=E(X^{2})-[E(X)]^{2}[/tex]
[tex]=3.08-(1.18)^{2}\\\\=1.6876[/tex]
Then the standard deviation is:
[tex]\text{Standard deviation}=\sqrt{\text{Variance}}[/tex]
[tex]=\sqrt{1.6876}\\\\=1.2990766\\\\\approx 1.30[/tex]
Thus, the mean and standard deviation for the random variable x are 1.18 and 1.30 respectively.
The correct option is (d).
Two competing gyms each offer childcare while parents work out Gym A charges $9.00 per hour of childcare. Gym B
charges $0.75 per 5 minutes of childcare. Which comparison of the childcare costs is accurate?
Answer:
They charge an equal amount of money each hour.
Answer:
Gym B and Gym A charge the same hourly rate for childcare.
Step-by-step explanation:
answer on edge
Solve the equation 3 Z + 5 = 35
Answer:
z=10 i hope this will help you
Step-by-step explanation:
3z+5=35
3z=35-5
3z=30
z=10
Answer:
Z = 10
Step-by-step explanation:
3Z+5=35
Subtract 5 from both sides
3Z=30
Divide both sides by 3
Z=10
A teacher wrote the equation 3y + 12 = 6x on the board. For what value of b would the additional equation 2y = 4x + b form a system of linear equations with infinitely many solutions?
b = –8
b = –4
b = 2
b = 6
Answer:
-8
Step-by-step explanation:
For a system to have infinitely many solutions the two equations must be the same line. We can simplify the first and second equations by dividing them by 3 and 2 respectively to get:
y + 4 = 2x
y = 2x + b/2 → y -b/2 = 2x
Since the constants must be equal, 4 = -b/2 which means b = -8.
Answer:
b=-8
Step-by-step explanation:
Please select the word from the list that best fits the definition
a leader of a group of people
Answer:
a sultan
Step-by-step explanation:
i looked it up on quizlet after thinking it was sultan and i was right
anyways the answer is sultan and its correct
have a good day!
Answer
the answer is sultan
Step-by-step explanation:
help me please!!!! Dan's car depreciates at a rate of 8% per year. By what percentage has Dan's car depreciated after 3 years? Give your answer to the nearest percent.
Answer:
22%
Step-by-step explanation:
Car's price is reduced by 8% or 0.92 times a year
after 3 years it will make:
0.92³= 0.778688≈ 0.78 timesor
0.78 = 1- 0.22price decrease = 22%Answer:
Hello!
Here is your answer:
22%
I hope I was able to help you. If not, please let me know!
Step-by-step explanation:
if the distance between sydney and goulburn is 200km, find the average speed to complete the journey in 2 hours and 30 minutes
Answer:
80 km/h
Step-by-step explanation:
2 h 30 min = 2.5 h
Average speed = distance/time= 200 km/2.5 h = 80 km/h
Aunit cube is shown.
Select the true statements
A unit cube can have a length of 1 inch, a width of 1 inch, and a height of 2 inches
A unit cube has one cubic unit of volume.
Another unit cube with the same length, width and height as the unit cube shown would have
the same volume
Aunit cube can be used to measure the weight of a rectangular prism.
A unit cube can be used to measure the volume of a rectangular prism.
Aunit cube can have a length of 4 feet, a width of 4 feet, and a height of 4 feet.
A unit cube can be used to determine the angle measures of a rectangular prism,
4 of 10 Answered
Session Timer: 11:03
Session Score: 259
Answer:
A unit cube has one cubic unit of volume.
Another unit cube with the same length, width and height as the unit cube shown would have the same volume
Step-by-step explanation:
A cube is a shape formed from the combination of a square.
A cube has equal sides.
But a unit cube has equal sides and equal volume to be equal to one, i.e unity.
Will pick brainliest! Please help with the attached file!
Answer:
25 degrees
Step-by-step explanation:
The value of an exterior angle is the difference between the two arcs that it forms divide by two. Therefore:
[tex]x+10=\dfrac{146-(6x+6)}{2}[/tex]
Multiply both sides by 2:
[tex]2x+20=146-6x-6[/tex]
Move all of the x's to one side:
[tex]8x+20=146-6[/tex]
Combine all of the constants on the other side:
[tex]8x=120[/tex]
Divide both sides by 8:
[tex]x=15[/tex]
Therefore, ECB=x+10=15+10=25 degrees.
Hope this helps!
Graph the line with slope -1/3 and y -intercept 6 .
Answer:
plot a point at 6 up from (0,0) and then go down one and over three places then plot another point- and so on - and so on
Step-by-step explanation:
To graph the line using the slope and intercept, first understand what the slope and intercept mean:
Slope is how steep or flat the line appears on the graph.
A very high or low slope (100 or -100) will be very steep on the graph.A slope very close to zero (0.0001 or -0.0001) will be very flat on the graph.A positive slope will travel northeast and southwest (for linear equations).A negative slope will travel northwest and southeast (for linear equations).The y-intercept is the point at which the line hits the y-axis. In this equation, the line hits the y-axis at positive 6, which means that the point is (0, 6).
You can use a method called "rise over run" to graph. The slope is negative one over three, so the line will "rise" negative one units after "running" three units.
So, for every one unit down, the line will travel three units to the right.
Graph this from the point (0, 6), your y-intercept, and plot the points according to the slope:
What would be the approximate 95% confidence interval for the mean number of ounces of catchup bottle in the sample
Answer:
The 95% confidence interval for the mean number of ounces of ketchup bottle is (23.8, 24.2).
Step-by-step explanation:
The complete question is:
Suppose that a restaurant chain claims that its bottles of ketchup contain 24 ounces of ketchup on average, with a standard deviation of 0.8 ounces. If you took a sample of 49 bottles of ketchup, what would be the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample?
Solution:
The (1 - α)% confidence interval for the population mean is:
[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\bar x=24\\\sigma=0.8\\n=49\\\text{Confidence Level}=95\%[/tex]
The critical value of z for 95% confidence level is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
*Use a z-table.
Compute the 95% confidence interval for the mean number of ounces of ketchup per bottle as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
[tex]=24\pm1.96\cdot \frac{0.80}{\sqrt{49}}\\\\=24\pm 0.224\\\\=(23.776, 24.224)\\\\\approx (23.8, 24.2)[/tex]
Thus, the 95% confidence interval for the mean number of ounces of ketchup bottle is (23.8, 24.2).
Mathematics: The graph below have the same shape. What is the equation of the blue graph?
Answer:
Since the blue graph is the red graph translated 3 units to the left the answer is D.
Find the value of y. -6y+14+4y=32
Answer:
So first subtract 14 from 32
That means that -6y+4y = 18
Simplify the left side 4-6=-2
-2y = 18
Divide by -2
-9 = y
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
-6y+14+4y=32
Combine like terms
-2y +14 = 32
Subtract 14 from each side
-2y +14-14 = 32-14
-2y =18
Divide each side by -2
-2y/-2 = 18/-2
y = -9
Graph g(x)=f(x+1) when f(x) =4x-2
[tex]g(x)=4(x+1)-2[/tex]
[tex]g(x)=4x+4-2[/tex]
[tex]g(x)=4x+2[/tex]
Image attached below for graph.
what is the value of x
14
15
16
17
Answer:
14
Step-by-step explanation:
Opposite angles in a rhombus are congruent. Even if you didn't know that, adding up the angles in this quadrilateral would tell you that ...
(5x)° = 70°
x = 70/5 = 14 . . . . . divide by 5
The value of x is 14.
