Answer:
5x+8y+2z = 68
Step-by-step explanation:
Given the point P0 = (2, 5, 9), to Find an equation for a plane through that point and normal to the vector n = 5i+8j+2k the following steps must be followed:
The equation for the plane passing through the point is expressed as;
a(x-x0)+b(y-y0)+c(z-z0) = 0 where;
(x0, y0, z0) is the point on the plane and (a,b,c) is the normal vector n.
Given the point (2, 5, 9) and normal vector n =(5, 8, 2)
x0 = 2, y0 = 5, z0 = 9, a = 5, b = 8 and c= 2.
Substituting this values into the equation of the plane above will give;
5(x-2)+8(y-5)+2(z-9) = 0
On expansion:
5x-10+8y-40+2z-18 = 0
5x+8y+2z-10-40-18 = 0
5x+8y+2z-68 = 0
The required equation of the plane is 5x+8y+2z = 68
Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Claim: The mean pulse rate (in beats per minute) of students in a large math class is greater than 71. A simple random sample of the students has a mean pulse rate of 71.7. Choose the correct answer below.
A. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
B. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
C. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
D. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
Answer:
The correct option is (D).
Step-by-step explanation:
In this case, we need to test whether the mean pulse rate (in beats per minute) of students in a large math class is greater than 71.
The hypothesis can be defined as follows:
H₀: The mean pulse rate of students in a large math class is not greater than 71, i.e. μ ≤ 71.
Hₐ: The mean pulse rate of students in a large math class is greater than 71, i.e. μ > 71.
It is provided that the sample mean pulse rate, of a simple random sample of the students is 71.7.
The sample mean is not very different from the population mean.
So, it cannot be said in confidence that the sample is unusual.
Thus, the correct option is (D).
"The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim."
To begin solving this system of linear equations by elimination you can add the equations. 3x + 2y = 38 5x – 2y = -30 8x = 8 This step works because of the A. distributive property B. commutative property 0 0 0 0 O c. multiplication property of equality O D. addition property equality
Answer:D
Step-by-step explanation:
Additive property big brain
This step works because of the addition of property equality.
What is adding the property of equality?The addition property of equality tells us that adding the identical wide variety to each facet of an equation offers us an equal equation. If a−b=c, then a−b+b=c+b,or a=c+b. The same goes with the subtraction belongings of equality
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Need help ASAP! What Is the measure of an angle If It Is 240 less then 6 times It’s own supplement?
Answer:
120°
Step-by-step explanation:
Given that an angle = 240 less than 6 × its own supplement,
Let x = be the angle
Its supplement = (180 - x)
If the angle (x) is 240 less than 6 times its own supplement, (180 - x), we will have the following expression:
[tex] x = 6*(180 - x) - 240 [/tex]
Simplify the expression to solve for x
[tex] x = 1080 - 6x - 240 [/tex]
[tex] x = 1080 - 240 - 6x [/tex]
[tex] x = 840 - 6x [/tex]
Add 6x to both sides
[tex] x + 6x = 840 - 6x + 6x [/tex]
[tex] 7x = 840 [/tex]
Divide both sides by 7 to solve for x
[tex] \frac{7x}{7} = \frac{840}{7} [/tex]
[tex] x = 120 [/tex]
Solve the inequality. –10d ≥ –70
Answer:
d≤7
Step-by-step explanation:
-10d≥-70
d≤7
[tex]{x}^{ log_{3}(x) } = 81 {x}^{3} [/tex]
can you solve by algebraically, not graphing and provide step by step explanation, please?
Answer:
x=81 or 1/3
Step-by-step explanation:
[tex]x^\log_3(x)} =81x^3\\\log_3(x^{\log_3(x)})=\log_3(81x^3)\\\(\log_3x)(\log_3x)=\log_381+\log_3x^3\\(\log_3x)^2=3\log_3x^+4\\\\Let u=\log_3x\\\\u^2-3u-4=0\\(u-4)(u+1)=0\\u=4 \\4=\log_3x\\x=3^4=81\\\\u=-1\\-1=\log_3x\\x=3^{-1}=1/3[/tex]
g Find the mean and the variance of the random variable X with probability function or density f(x) of a uniform distribution on [0, 8].
Answer: E(X) = 4
V(X) = [tex]\frac{16}{3}[/tex]
Step-by-step explanation: An uniform distribution is a random variable X restricted to a finite interval [a,b] and has a constant function f(x) over this interval, i.e., the function is of form:
f(x) = [tex]\left \{ {{\frac{1}{b-a} } \atop {0}} \right.[/tex]
The mean or expectation of an unifrom distribution is:
E(X) = [tex]\int\limits^b_a {x.f(x)} \, dx[/tex]
For the density function in interval [0,8], expectation value is:
E(X) = [tex]\int\limits^8_0 {x.(\frac{1}{8-0} )} \, dx[/tex]
E(X) = [tex]\int\limits^8_0 {\frac{x}{8} } \, dx[/tex]
E(X) = [tex]\frac{1}{8}. \int\limits^8_0 {x} \, dx[/tex]
E(X) = [tex]\frac{1}{8}.(\frac{x^{2}}{2} )[/tex]
E(X) = [tex]\frac{1}{8} (\frac{8^{2}}{2} )[/tex]
E(X) = 4
Variance of a probability distribution can be written as:
V(X) = [tex]E(X^{2}) - [E(X)]^{2}[/tex]
For uniform distribution in interval [0,8]:
V(X) = [tex]\int\limits^b_a {x^{2}.\frac{1}{8-0} } \, dx - (\frac{8+0}{2})^{2}[/tex]
V(X) = [tex]\frac{1}{8} \int\limits^8_0 {x^{2}} \, dx - 4^{2}[/tex]
V(X) = [tex]\frac{1}{8} (\frac{x^{3}}{3} ) - 16[/tex]
V(X) = [tex]\frac{1}{8} (\frac{8^{3}}{3} ) - 16[/tex]
V(X) = [tex]\frac{64}{3}[/tex] - 16
V(X) = [tex]\frac{16}{3}[/tex]
The mean and variance are 4 and 16/3, respectively
The LARGEST prime number that is less than 100 is
(A) 91
(B) 93
(C) 97
(D) 99
Answer:
97
Step-by-step explanation:
ez
Answer:
(c) 97
Step-by-step explanation:
97 is the largest prime number because 97 has no other multiples other than 1 and itself. 99 is divisible by 3, 9, 11, 33, 99.
91 is a prime number but it is not the greatest.
93 is a composite.
99 is a composite as well.
What is the measure of A? (solve to the nearest WHOLE DEGREE)
Answer:
A = 0.507 or 29 degrees
Step-by-step explanation:
5 = tanA * 9
inv tan = 5/9
angle A = 0.507
angle A = 29 degrees
You pick two students at random, one at a time. What is the probability that the second student is a sophomore, given that the first is a freshman
Answer:
0.40
Step-by-step explanation:
The computation of the probability for the second student be sophomore and the first is a freshman is shown below:
Let us assume
Sophomore = S
Freshman = F
Based on this assumption, the probability is as follows
So,
[tex]= \frac{P(S\cap F)}{P(F)} \\\\ = \frac{P(S) \times P(F)}{P(F)} \\\\ = \frac{16}{40}[/tex]
= 0.40
Hence, the probability for the second student be sophomore and the first student be freshman is 0.40
Which question is best modeled with a division expression? What is the sum of 3 and StartFraction 8 Over 11 EndFraction? What is the quotient of 3 and StartFraction 8 Over 11 EndFraction? What is the product of 3 and StartFraction 8 Over 11 EndFraction? What is the difference of 3 and StartFraction 8 Over 11 EndFraction?
Answer: B
Step-by-step explanation:
The sum, quotient, product, and difference of the numbers 3 and 8/11 will be 3.7272, 4.125, 2.1818, and 2.2727 respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The numbers are given below.
3 and 8/11
The sum of the numbers is calculated as,
⇒ 3 + 8/11
⇒ (33 + 8) / 11
⇒ 41 / 11
⇒ 3.7272
The quotient of the numbers is calculated as,
⇒ 3 / (8/11)
⇒ 3 x 11 / 8
⇒ 4.125
The product of the numbers is calculated as,
⇒ (3) x (8 / 11)
⇒ 24 / 11
⇒ 2.1818
The difference between the numbers is calculated as,
⇒ 3 - 8/11
⇒ (33 - 8) / 11
⇒ 25 / 11
⇒ 2.2727
The sum, quotient, product, and difference of the numbers 3 and 8/11 will be 3.7272, 4.125, 2.1818, and 2.2727 respectively.
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the exact derivative of f(x)=x^3 at x=5
Answer:
[tex]75[/tex]
Step-by-step explanation:
[tex]\frac{d}{dx}\left(x^3\right)[/tex]
[tex]=3x^{3-1}[/tex]
[tex]=3x^2[/tex]
[tex]3\left(5\right)^2[/tex]
[tex]=3\cdot \:25[/tex]
[tex]=75[/tex]
Shannon went to an auto repair shop and paid $339.50, which included parts that cost $112 and 3.5 hours of labor. Joni went to an auto repair shop and paid $455, which included parts that cost $310 and 2.5 hours of labor. Which correctly compares the cost of the labor? Shannon paid $7 more per hour for labor. Shannon paid $7 less per hour for labor. Joni paid $85 more per hour for labor. Joni paid $85 less per hour for labor.
for labor. Joni paid $85 less per hour for labor. explanation:
The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.
What is the cost?It refers to the total amount of the expenditure done on a product in manufacturing or procuring.
What is labor cost?It refers to the expenditure done on procuring labor for the work.
How to calculate per hour labor cost?In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,
labor cost Shannon Paid=339.50-112
=$227.50
labor cost per hour=227.50/3.5
=$6.5 per hour
Joni paid total $455 in which the cost of spare parts is $310 and rest is labor
labor cost paid by Joni=455-310
=$145
labor cost per hour=145/2.5
=$58 per hour
So by doing comparing we found that Shannon had paid $6 per hour extra for labor.
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which graph represents a function?
I can determine a function by drawing a vertical line. If this line pass trought the graph only one time, it's a function.
The only function there is the last one. (Right bottom)
In order to estimate the average time spent on the computer terminals per student at a university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation is 1.8 hours. With a 0.95 probability, the margin of error is approximately
Answer:
The margin of error is approximately 0.39.
Step-by-step explanation:
Formular for the margin of error is
Margin of error = z* (sd/√n)
Where z* is 95% confidence level = 1.96, sd is 1.8 and n is 81
Margin of error = 1.96 (1.8/√81)
= 1.96(1.8/9)
= 1.96*0.2
= 0.392
What is the range of the function f(x)=3/4|x|-3
Range is [tex]y\in[-3,+\infty)[/tex].
Hope this helps.
???????????????????
?
?
?
?
Answer:
It should be 10 for the first box, 1000 for the second box and 100 for the third box.
Step-by-step explanation:
Each extra decimal place value added, u have to multiply it by the next value place such as tenths/hundreths/thousandths
It has been estimated that as many as 70% of the fish caught in certain areas of the Great Lakes have liver cancer due to the pollutants present. Find an approximate 95% range for the percentage of fish with liver cancer present in a sample of 130 fish.
Answer:
62.12% to 77.88%
Step-by-step explanation:
We proceed as follows mathematically;
From the question
n=130
Estimate for sample proportion=70% = 70/100 = 0.7 = p
Level of significance is =1-0.95=0.05
Z critical value(using Z table)=1.96
Confidence interval formula is ;
p ± Z * √(p(1-p)/n
= 0.70 ± √(0.7(1-0.7)/130
=(0.6212,0.7788)
Lower confidence interval limit =0.6212
Upper confidence interval limit =0.7788
In percentages , we simply multiply by 100 in both cases =
62.12 % to 77.88%
The rule r_y-axis ° R_0,90 (x,y) is applied to ABC. Which triangle shows the final image?
a. 1
b. 2
c. 3
d. 4
Answer: 4
Step-by-step explanation:
Simply rotate the graph 1-turn to the left to see where the triangle lands. The x-axis will be the horizontal line and the y-axis will be the vertical line.
The attachment shows the graph rotated 1-turn to the left (90°).
Notice it is in the exact same position as #4.
Given the center of a circle is (0, -4) and the radius is 5, which of the following would be the correct equation?
Answer:
x^2+(y+4)^2=25
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Step-by-step explanation:
A rhombus has interior angle measures of 104∘, 104∘, 76∘ and X degrees. Find the measure of angle X in the rhombus. Enter only the number of degrees in the answer box. Angle X measures degrees.
Answer:
76°
Interior angle of a rhombus =360
104° +104° +76° +X =360
X= 360 - 284
X= 76°
We know that the value of ∠x in the given rhombus is 76°.
What is a rhombus?A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal. A rhombus' internal angles add up to 360 degrees, just like in other quadrilaterals, and, like in a parallelogram, the angles of opposite pairs of vertices are identical. The total of the angles of two neighboring vertices is 180 degrees.So, get the ∠x as follows:
We now know that sum of all angles in a rhombus is 360°.Then,
104 + 104 + 76 + x = 360284 + x = 360x = 360 - 284x = 76°Therefore, we know that the value of ∠x in the given rhombus is 76°.
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Multiply the rational expressions: Divide the rational expressions:
Answer:
1). [tex]\frac{2}{(x+1)}[/tex]
2). [tex]\frac{x^2}{2(x+1)}[/tex]
Step-by-step explanation:
For multiplication of the rational expressions,
[tex]\frac{x}{(x+1)}\times \frac{2}{x}[/tex]
= [tex]\frac{2x}{x(x+1)}[/tex]
= [tex]\frac{2}{(x+1)}[/tex]
For division of the rational expressions,
[tex]\frac{x}{(x+1)}\div \frac{2}{x}[/tex]
= [tex]\frac{x}{(x+1)}\times \frac{x}{2}[/tex]
= [tex]\frac{x^2}{2(x+1)}[/tex]
[When the divisor is a rational expression or a rational number, we change the sign from division to multiplication and reciprocate or flip the fraction.
This is applicable for division of the rational expressions only].
A dress regularly sells for $137. The sale price is $102.75. Find the discount & the percent of the discount
Answer:
Discount : $34.25 off. Percent of the discount : 25%
Step-by-step explanation:
137 - 102.75 = 34.25.
34.25/137 x 100 = 25%
Can you help me solve this question? (Also explain me how is it possible)
Answer:
Answer B) (2 times )
Step-by-step explanation:
Let's start with the person that shook hands more (Dora), so we already know how four of this connections took place See attached image.
step 1:
D is connected to A, B, C, and E
Step 2:
Now proceed with the connections for the second greatest (C who shook hands with 3 people). Notice that C is already connected with D, and can connect with B and with E, but NOT with A (since this person shook hands only once - with D. So C is connected to B, D, and E completing the three handshakes.
step 3: Now just corroborate that B is already connected to two people (C and D). So just count the number of connections that E is left with: 2 handshakes.
Answer:
( E ) 0
Step-by-step explanation:
Solution:-
- There can be two ways in solving this question. Either we lay-out a map of every person ( Alan, Bella, Claire, Dora, and Erik ) shaking hands with each other.
- We will use an intuitive way of tackling this problem.
- We have a total of 5 people who greeted each other at the party.
- Each of the 5 people shook hands exactly " once "! We can give this a technical term of " shaking hands - without replacement ".
- We will define our event as shaking hands. It takes 2 people to shake hands.
- We will try to determine the total number of unique "combinations" that would result in each person shaking hands exactly one time.
- We have a total of 5 people and we will make unique combinations of 2 people shaking hands. This can be written as:
5C2 = 10 possible ways.
- So there are a total of 10 possible ways for 5 people to greet each other exactly once at the party.
- We are already given the data for how many handshakes were made by each person as follows:
Name Number of handshakes
Alan 1
Bella 2
Claire 3
Dora 4
=======================================
Total 10
=======================================
- So from the data given. 10 unique hand-shakes were already done by the time it was " Eriks " turn to go and greet someone. This also means that Erik has already met all 4 people in that party. So he doesn't have to approach anyone to shake hands and know someone. He is already been introduced to rest of 4 people in the group.
Answer: Erik does not need to shake hands with anyone! He is known and greeted rest of the 4 people on the group.
Given that is both the median and altitude of , congruence postulate SAS is used to prove that is what type of triangle?
A.
equilateral
B.
scalene obtuse
C.
isosceles
D.
scalene acute
Answer:isosceles is the correct
Step-by-step explanation:
According to the given conditions the triangle ABC is an isosceles triangle.
What is an isosceles triangle?An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.
Given that, BD is median and altitude in the triangle ABC, and we are asked to find that what type of the triangle ABC will be if we prove triangles ADB and CBD congruent by SAS rule,
So, the proof is as follows,
AD = CD [definition of median]
∠ ADB = ∠ CDB [definition of altitude]
BD = BD [reflexive property]
∴ Δ ADB ≅ Δ CBD by SAS rule
AB = BC by CPCT
According to the definition of an isosceles triangle we can say that, ABC is an isosceles triangle.
Hence, according to the given conditions the triangle ABC is an isosceles triangle.
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The lines shown below are parallel.if the green line has a slope of -1,what is the slope of the red line?
Answer:
-1
Step-by-step explanation:
If a line is parallel on a graph, then that means that they will descend/climb at the same rate. Therefore, the slope of this line is also -1.
Hope this helped!
Answer:If they are parallel,
Then their slope will be same...
Step-by-step explanation:
A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 14 respectively. The standard error of the mean is
Answer:
1.4Step-by-step explanation:
The formula for calculating the standard error of the mean is expressed as shown below;
Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex]
[tex]\sigma[/tex] is the standard deviation and n is the sample size.
Given [tex]\sigma[/tex] = 14 and n = 100
Substituting this values into the formula fr calculating the standard error of the mean;
[tex]SE = \frac{14}{\sqrt{100} } \\\\SE = \frac{14}{10} \\\\SE = 1.4[/tex]
Hence, standard error of the mean is 1.4
Quadrilateral RSTQ is a parallelogram.
R
Which of the following relationships must be true?
O RS = RO
O TQ QR
O ZT ZR
O ZSRR
Answer:
[tex]\angle T \cong \angle R\\\angle S \cong \angle Q[/tex]
Step-by-step explanation:
According to the Parallelogram definition, every Parallelogram have a pair of congruent sides. In this case, Namely [tex]\overline{RS} \cong \overline{TQ}[/tex] and [tex]\overline{QR} \cong \overline{TS}[/tex]
(not listed as an option)
And the opposite angles are congruent too.
So
[tex]\angle T \cong \angle R\\\angle S \cong \angle Q[/tex]
∠R≅∠T relationship is true for the RSTQ parallelogram
What is Quadrilateral?A quadrilateral is a polygon having four sides, four angles, and four vertices.
A parallelogram is a quadrilateral with four sides.
a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
In parallelogram the opposite sides have equal length.
The opposite sides are congruent and the opposite angles are also congruent.
SR=TQ
ST=RQ
These sides are equal and
∠R≅∠T
∠S≅∠Q
In the given options only ∠R≅∠T is given, so we can consider this.
Hence ∠R≅∠T relationship is true for the RSTQ parallelogram
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Compute the mean and variance of the following probability distribution. (Round your answers to 2 decimal places.) x P(x) 6 0.10 12 0.35 18 0.25 24 0.30
Answer:
Mean = 16.5
Variance = 35.55
Step-by-step explanation:
x P(x) x. P(x) x² x². P(x)
6 0.10 0.6 36 3.6
12 0.35 4.2 144 50.4
18 0.25 4.5 324 81
24 0.30 7.2 576 172.8
∑x P (x) 16.5 ∑x² P (x) 307.8
The expected value of x E[X] gives the mean where X is the discrete random variable with the given probabilities.
Mean is given by E(X)= ∑x P (x) = 16.5
Similarly the variance is also calculated using the expected value of X and X².
Variance is given= E(X)²- [E(X)]²= 307.8- (16.5)²= 307.8-272.25 = 35.55
The volume of a spherical cancerous tumor is given by the following equation. V(r) =(4/3)pi r^3 If the radius of a tumor is estimated at 1.4 cm, with a maximum error in measurement of 0.005 cm, determine the error that might occur when the volume of the tumor is calculated:___________.
Answer:
The error that might occur is [tex]\±0.123cm^3[/tex]
Step-by-step explanation:
Given
[tex]V = \frac{4}{3}\pi r^3[/tex]
[tex]Radius,\ r = 1.4cm[/tex]
[tex]Error = 0.005cm[/tex]
Required
Determine the error that might occur in the volume of the tumor
Given that there's an error in measurement, this question will be solved using the concept of differentiation;
First, we'll rewrite the given parameters in differentiation notations;
[tex]r = 1.4[/tex] --- Radius
[tex]dV = \±0.005[/tex] --- Change in measurement
[tex]V(r) = \frac{4}{3}\pi r^3[/tex] --- Volume as a function of radius
The relationship between the above parameters is as follows;
[tex]\frac{dV}{dr} = V'(r)[/tex]
This can be rewritten as
[tex]\frac{dV}{dr} = (V(r))'[/tex]
Substitute [tex]\frac{4}{3}\pi r^3[/tex] for [tex]V(r)[/tex]
[tex]\frac{dV}{dr} = (\frac{4}{3}\pi r^3)'[/tex]
Multiply both sides by dr
[tex]dr * \frac{dV}{dr} = (\frac{4}{3}\pi r^3)' * dr[/tex]
[tex]dV = (\frac{4}{3}\pi r^3)' * dr[/tex]
[tex]dV = \frac{4}{3}\pi( r^3)' dr[/tex]
Differentiate
[tex]dV = \frac{4}{3}\pi( r^3)' dr[/tex]
[tex]dV = \frac{4}{3}\pi* 3r^2\ dr[/tex]
[tex]dV = 4\pi* r^2\ dr[/tex]
Substitute the values of r, dr and take [tex]\pi[/tex] as 3.142
[tex]dV = 4 * 3.142* 1.4^2 * \±0.005[/tex]
[tex]dV = \±0.1231664[/tex]
[tex]dV = \±0.123[/tex] (Approximated)
Hence, the error that might occur is ±0.123
Which could be used to evaluate the expression
43)
O (-6)(4)+(-01
0 (-6)(4) «(-6) (
3
O (-6+4)+ -6
G
0 (-6+4)*|-6-
Answer:
[tex] (-6)(4) + (-6)(\frac{2}{3}) [/tex]
Step-by-step explanation:
The expression, [tex] -6(4\frac{2}{3}) [/tex] , can be understood or interpreted as negative six multiplied by four and two-third.
Thus, it could be evaluated using distributive property of multiplication, as shown below:
[tex] (-6)(4) + (-6)(\frac{2}{3}) [/tex]
[tex](-6)(4) + (-6)(\frac{2}{3}) \\(-24) + (-2)(2)\\-24 + (-4)\\-24 - 4\\= -28[/tex]