Answer: See below
*Note: I was not sure is -4² was -4² or (-4)². I have done the problem both ways. You should see the problem you are supposed to solve by looking at the 2 different equations below.
Step-by-step explanation:
The problem states -4²+(5-2)(-6). Now, this can be interpreted in another way. The key is the -4². This can also be (-4)². You get a completely different answer. Since the problem seemed like the first option, I will still do it both ways to make sure you can see the difference. If you meant (-4)², then you would still get an explanation.
-4²+(5-2)(-6)
-16+(3)(-6)
-16+(-18)
-34
_________________________________________________________
(-4)²+(5-2)(-6)
16+(3)(-6)
16+(-18)
-2
As you can see, both answers are very different. The -4 matters whether there are parentheses or not.
The height of a certain plant is determined by a dominant allele T corresponding to tall plants, and a recessive allele t corresponding to short (or
dwarf) plants. If both parent plants have genotype Tt, compute the probability that the offspring plants will be tall. Hint: Draw a Punnett square.
(Enter your probability as a fraction.)
Answer:
The probability of the plants being tall is equal to P(TT) + P(Tt)= 1/4+1/2=3/4
Step-by-step explanation:
Hello!
The characteristic "height" of a plant is determined by the alleles "tall" T (dominant) and "short" a (recessive). If both parents are Tt, you have to calculate the probability of the offspring being tall (TT or Tt)
To construct the Punnet square you have to make a table, where the parental alleles will be in the margins, for example: the father's alleles in the columns and the mother's alleles in the rows.
Each parent will produce a haploid gamete that will carry one of the alleles, so the probability for the offspring receiving one of the alleles is 1/2
Father (Tt): gametes will carry either the dominant allele T or the recessive allele t with equal probability 1/2
Mother (Tt): gametes will also carry either the dominant allele T or the recessive allele t with equal probability 1/2
Then you have to cross each allele to determine all possible outcomes for the offsprings. For each cell, the probability of obtaining both alleles will be the product of the probability of each allele (See attachment)
First combination, the offspring will receive one dominant allele from his father and one dominant allele from his mother: TT, the probability of obtaining an offspring with this genotype will be P(T) * P(T) = 1/2*1/2=1/4
Second combination, the offspring will receive the recessive allele from the father and the dominant allele from the mother, then its genotype till be tT with probability: P(t)*P(T)= 1/2*1/2=1/4
Third combination, the offspring will receive one dominant allele from his father and one recessive allele from his mother, the resulting genotype will be Tt with probability: P(T)*P(t)= 1/2*1/2=1/4
Combination, the offspring will receive both recessive alleles from his parents, the resulting genotype will be tt with probability: P(t)*P(t)= 1/2*1/2=1/4
So there are three possible genotypes for the next generation:
TT with probability P(TT)= 1/4
Tt with probability: P(Tt)+P(tT)=1/4+1/4=1/2⇒ This genotype is observed twice so you have to add them.
tt with probability P(tt)= 1/4
Assuming this genotype shows complete dominance, you'll observe the characteristic "Tall" in individuals that carry the dominant allele "T", i.e. individuals with genotype "TT" and "Tt"
So the probability of the plants being tall is equal to P(TT) + P(Tt)= 1/4+1/2=3/4
I hope this helps!
When a frequency distribution is exhaustive, each individual, object, or measurement from a sample or population must appear in at least one category.
a. True
b. False
Answer:
a. True
Step-by-step explanation:
The frequency distribution is a summary of the gathered data set, in which the interval of values is divided into classes.
A requirement for a frequency distribution is for the classes to be mutually exclusive and exhaustive. That is, each individual, object, or measurement in the data set must belong to one and only one class.
Then, we can conclude that each individual, object, or measurement must appear in at least one (in fact, only in one) category or class.
Use the graphing calculator to graph the line y = 2x – 7.
Use the graph to find the missing coordinates below.
(4.75, )
(, –7.7)
(0.4, )
Answer:
(4.75, 2.5), (-0.35, -7.7), (0.4, -6.2)
Step-by-step explanation:
Given the line
[tex]y = 2x- 7[/tex]
Given the missing coordinates:
(4.75, )
(, –7.7)
(0.4, )
We know that every coordinate is of the form [tex](x,y)[/tex].
So, we can easily solve the for other variable if one variable is given from the given line using the graph or the given equation.
For the first coordinate:
(4.75, )
From graph it can be found that y = 2.5
Verifying using the equation.
Putting the value of x = 4.75 in the equation we get:
y = 2[tex]\times[/tex] 4.75 - 7
y = 9.5 - 7 = 2.5
So, the coordinate is (4.75, 2.5)
For the second coordinate:
(, -7.7 )
From graph it can be found that x = -0.35
Verifying using the equation:
Putting the value of y = -7.7 in the equation we get:
-7.7 = 2x - 7
2x = -7.7 + 7 = -0.7
x = -0.35
So, the coordinate is (-0.35, -7.7).
For the third coordinate:
(0.4, )
From graph it can be found that y = -6.2
Verifying using the equation.
Putting the value of x = 0.4 in the equation we get:
y = 2[tex]\times[/tex] 0.4 - 7
y = 0.8 - 7 = -6.2
So, the coordinate is (0.4, -6.2)
Also, please refer to the attached graph.
So, the answer is:
(4.75, 2.5), (-0.35, -7.7), (0.4, -6.2)
Answer: its 2.5, -0.35, -6.2
Step-by-step explanation: in easier words
Given the equation 4x - 3y = 12
1. Write the equation in slope-intercept form.
2. Identify the slope and y-intercept.
3. Graph the line.
4. Identify if it is a positive or negative slope.
Answer:
see below
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
4x - 3y = 12
Solve for y
Subtract 4x from each side
4x-4x - 3y =-4x+ 12
-3y = -4x+12
Divide by -3
-3y/-3 = -4x/-3 + 12/-3
y = 4/3x -4
The slope is 4/3 and the y intercept is -4
The slope is Positive
After scoring a touchdown, a football team may elect to attempt a two-point conversion, by running or passing the ball into the end zone. If successful, the team scores two points. For a certain football team, the probability that this play is successful is 0.40.
a.â Let X =1 if successful, X= 0 if not. Find the mean and variance of X.
b.â If the conversion is successful, the team scores 2 points; if not the team scores 0 points. Let Y be the number of points scored. Does Y have a Bernoulli distribution? If so, find the success probability. If not, explain why not.
c.â Find the mean and variance of Y.
Answer:
a) Mean of X = 0.40
Variance of X = 0.24
b) Y is a Bernoulli's distribution. Check Explanation for reasons.
c) Mean of Y = 0.80 points
Variance of Y = 0.96
Step-by-step explanation:
a) The probability that play is successful is 0.40. Hence, the probability that play isn't successful is then 1 - 0.40 = 0.60.
Random variable X represents when play is successful or not, X = 1 when play is successful and X = 0 when play isn't successful.
The probability mass function of X is then
X | Probability of X
0 | 0.60
1 | 0.40
The mean is given in terms of the expected value, which is expressed as
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
Mean = E(X) = (0 × 0.60) + (1 × 0.40) = 0.40
Variance = Var(X) = Σx²p − μ²
μ = mean = E(X) = 0.40
Σx²p = (0² × 0.60) + (1² × 0.40) = 0.40
Variance = Var(X) = 0.40 - 0.40² = 0.24
b) If the conversion is successful, the team scores 2 points; if not the team scores 0 points. If Y ia the number of points that team scores.Y can take on values of 2 and 0 only.
A Bernoulli distribution is a discrete distribution with only two possible outcomes in which success occurs with probability of p and failure occurs with probability of (1 - p).
Since the probability of a successful conversion and subsequent 2 points is 0.40 and the probability of failure and subsequent 0 point is 0.60, it is evident that Y is a Bernoulli's distribution.
The probability mass function for Y is then
Y | Probability of Y
0 | 0.60
2 | 0.40
c) Mean and Variance of Y
Mean = E(Y)
E(Y) = Σ yᵢpᵢ
yᵢ = each variable
pᵢ = probability of each variable
E(Y) = (0 × 0.60) + (2 × 0.40) = 0.80 points
Variance = Var(Y) = Σy²p − μ²
μ = mean = E(Y) = 0.80
Σy²p = (0² × 0.60) + (2² × 0.40) = 1.60
Variance = Var(Y) = 1.60 - 0.80² = 0.96
Hope this Helps!!!
the diagram shows a regular decagon please help
Answer:
36°
Step-by-step explanation:
[tex]size \: of \: one \: exterior \: angle \\ \\ = \frac{360 \degree}{no \: of \: sides} \\ \\ = \frac{360 \degree}{10} \\ \\ = 36 \degree[/tex]
Answer:
Exterior Angle = 36 degrees
Step-by-step explanation:
The measure of each interior angle of the decagon is 144
So,
Exterior Angle = 180 - 144 (Interior and Exterior angles are angles on a straight line hence adding up to 180 degrees)
Exterior Angle = 36 degrees
A veterinarian is enclosing a rectangular outdoor running area against his building for the dogs he cares for. He needs to maximize the area using 100 feet of fencing. The quadratic function A(x)=x(100−2x) gives the area, A, of the dog run for the length, x, of the building that will border the dog run. Find the length of the building that should border the dog run to give the maximum area, and then find the maximum area of the dog run.
Answer:
a) The length of the building that should border the dog run to give the maximum area = 25feet
b) The maximum area of the dog run = 1250 s q feet²
Step-by-step explanation:
Step(i):-
Given function
A(x) = x (100-2x)
A (x) = 100x - 2x²...(i)
Differentiating equation (i) with respective to 'x'
[tex]\frac{dA}{dx} = 100 (1) - 2 (2x)[/tex]
⇒ [tex]\frac{dA}{dx} = 100 - 4 x[/tex] ...(ii)
Equating zero
⇒ 100 - 4x =0
⇒ 100 = 4x
Dividing '4' on both sides , we get
x = 25
Step(ii):-
Again differentiating equation (ii) with respective to 'x' , we get
[tex]\frac{d^{2} A}{dx^{2} } = -4 (1) < 0[/tex]
Therefore The maximum value at x = 25
The length of the building that should border the dog run to give the maximum area = 25
Step(iii)
Given A (x) = x ( 100 -2 x)
substitute 'x' = 25 feet
A(x) = 25 ( 100 - 2(25))
= 25(50)
= 1250
Conclusion:-
The maximum area of the dog run = 12 50 s q feet²
What is the range of the function shown on the graph above?
Answer:
-9≤y≤8
Step-by-step explanation:
The range is the output values
Y goes from -9 to 8
-9≤y≤8
Answer:
-9≤y≤8
Step-by-step explanation:
That is the correct answer on plato.
One rule of thumb in the fast-food restaurant business is a "4 times markup": The price of a food item should be four times the price of the ingredients used in making the item. If the cost of ingredients used in making a taco is 1.5 dollars, what should be the price of the taco?
Answer:
The price of taco should be $6
Step-by-step explanation:
The rule is that the price of a food item should be four times the price of the ingredients used in making the food item.
mathematically,
[tex]y = 4x[/tex]
where [tex]y[/tex] is the price of the food item
[tex]x[/tex] is the price of the ingredients
If the price of ingredients for making taco is 1.5 dollars
price of taco = ?
substituting into the equation
[tex]y[/tex] = 4(1.5) = $6
(2.8(2 4/5 ·(8.75−2 1/2 )))·7.25−3 3/4
Answer:
351.5
Step-by-step explanation:
Step 1: Convert fractions to improper
(2.8(14/5(8.75 - 5/2)))7.25 - 15/4
Step 2: Parenthesis
(2.8(14/5(6.25)))7.25 - 15/4
Step 3: Parenthesis
(2.8(17.5))7.25 - 15/4
Step 4: Parenthesis
49(7.25) - 15/4
Step 5: Multiply
355.25 - 15/4
Step 6: Subtract
351.5
Suppose that $n, n+1, n+2, n+3, n+4$ are five consecutive integers. Determine a simplified expression for the sum of these five consecutive integers.
Answer:
5n + 10
Step-by-step explanation:
We would like to find the sum of these 5 integers. Simply add them up:
n + (n + 1) + (n + 2) + (n + 3) + (n + 4) = 5n + (1 + 2 + 3 + 4) = 5n + 10
The answer is thus 5n + 10.
~ an aesthetics lover
Answer:
5n + 10
Step-by-step explanation:
We need to add the five consecutive integers.
n + n + 1 + n + 2 + n + 3 + n + 4
Rearrange.
n + n + n + n + n + 1 + 2 + 3 + 4
Add.
5n + 10
One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a -credit course, a B in each of -credit courses, a C in a -credit course, and a D in a -credit course?
Question Correction
One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a 3-credit course, a B in each of three 4-credit courses, a C in a 2-credit course, and a D in a 3-credit course?
Answer:
2.75
Step-by-step explanation:
We present the information in the table below.
[tex]\left|\begin{array}{c|c|c|c}$Course Grade&$Grade Point(x)&$Course Credit(y)&$Product(xy)\\---&---&---&---\\A&4&3&12\\B&3&4&12\\B&3&4&12\\B&3&4&12\\C&2&2&4\\D&1&3&3\\---&---&---&---\\$Total&&20&55\end{array}\right|[/tex]
Therefore, the GPA of the student is:
[tex]GPA=\dfrac{55}{20}\\\\ =2.75[/tex]
The smaller of two numbers is one-half the larger, and their sum is 27. Find the
numbers.
Answer:
9 and 18
Step-by-step explanation:
The numbers are in the ratio 1 : 2, so the ratio of the smaller to the total is ...
1 : (1+2) = 1 : 3
1/3 of 27 is 9, the value of the smaller number. The larger number is double this, so is 18.
The numbers are 9 and 18.
Answer:
9 and 18
Step-by-step explanation:
you know the explanation since another guy put it
About ____% of the area is between z= -2 and z= 2 (or within 2 standard deviations of the mean)
Answer:
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
Step-by-step explanation:
Explanation:-
Given data Z = -2 and Z =2
The probability that
P( -2 ≤Z ≤2) = P( Z≤2) - P(Z≤-2)
= 0.5 + A(2) - ( 0.5 - A(-2))
= A (2) + A(-2)
= 2 × A(2) (∵ A(-2) = A(2)
= 2×0.4772
= 0.9544
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
One of the solutions to x2 − 2x − 15 = 0 is x = −3. What is the other solution?
20 points if you can answer in under 30 minuets
Answer:
x=5 x=-3
Step-by-step explanation:
x^2 − 2x − 15 =0
Factor
What two numbers multiply to -15 and add to -2
-5*3 = -15
-5+3 =-2
(x-5) (x+3)=0
Using the zero product property
x-5 =0 x+3 =0
x=5 x=-3
Answer:
x^2 - 2x - 15 = 0
(x - 5) (x + 3) = 0
x - 5 = 0
x = 5
x + 3 = 0
x = -3
A child is 2 -1/2 feet tall. The child’s mother is twice as tall as the child. How tall is the child’s mother
Answer:
5 feet
Step-by-step explanation:
"Twice as tall" means "2 times as tall".
2 × (2 1/2 ft) = (2 × 2 ft) +(2 × (1/2 ft)) = 4 ft + 1 ft = 5 ft
The child's mother is 5 feet tall.
Answer:
The mother is 5ft tall
Step-by-step explanation:
2 1/2 + 2 1/2 = 5ft
2ft+2ft = 4ft
1/2+1/2= 1ft
4ft+1ft = 5ft
Don’t understand this, if anyone can help that would be awesome. :)
Answer:
look up the basic rules for sin and cos
Step-by-step explanation:
the required condition for using an anova procedure on data from several populations for mean comparison is that the
Answer:
The sampled populations have equal variances
Step-by-step explanation:
ANOVA which is fully known as Analysis of variances can be defined as the collection of statistical models as well as their associated estimation procedures which enables easily and effectively analyzis of the differences among various group means in a sample reason been that ANOVA is a total variance in which the observed variance in a specific variable is been separated into components which are attributable to various sources of variation which is why ANOVA help to provides a statistical test to check whether two or more population means are equal.
Therefore the required condition for using an ANOVA procedure on data from several populations for mean comparison is that THE SAMPLED POPULATION HAVE EQUAL VARIANCE.
Anita works at a local news station and needs to decide which news story to report first. Of the news stories, 3 are local, 4 are international, and 5 national. The stories are equally important so anita randomly orders the stories. What is the probability that the first story is a national story. Give your answer as a fraction
For the functions f(x)=3x−1 and g(x)=4x−3, find (f∘g)(x) and (g∘f)(x)
The mean height of women in a country (ages 20-29) is 63.5 inches. A random sample of 50 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume the standard deviation equals 2.96.
Answer:
11.70% probability that the mean height for the sample is greater than 64 inches
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this question:
[tex]\mu = 63.5, \sigma = 2.96, n = 50, s = \frac{2.96}{\sqrt{50}} = 0.4186[/tex]
What is the probability that the mean height for the sample is greater than 64 inches?
This is 1 subtracted by the pvalue of Z when X = 64.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64 - 63.5}{0.4186}[/tex]
[tex]Z = 1.19[/tex]
[tex]Z = 1.19[/tex] has a pvalue of 0.8830
1 - 0.8830 = 0.1170
11.70% probability that the mean height for the sample is greater than 64 inches
Please answer this correctly
Answer:
2/3
Step-by-step explanation:
There are 2 numbers out of 3 that fit the rule, 1 and 3. There is a 2/3 chance picking one of them.
Answer:
2/3Step-by-step explanation:
This is the answer because one number that is select is one. A number greater than 2 is 3. SO it is 2/3.
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.050.05. If 212212 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.030.03
Answer:
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes 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]
In this question:
[tex]p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 0.03?
This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So
X = 0.08
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.08 - 0.05}{0.015}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 0.02
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.02 - 0.05}{0.015}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.
Create a transformation that is not a similarity transformation. Use coordinate notation .
Answer:
(x, y) ⇒ (2x, y)
Step-by-step explanation:
Any rigid transformation or dilation will be a similarity transformation. A transformation that doesn't preserve similarity will be none of those, so may be non-linear or different in one direction than another.
Several possibilities come to mind:
(x, y) ⇒ (2x, y) . . . . . . stretches x, but not y
(x, y) ⇒ (x+y, y) . . . . . a "shear" transformation
(x, y) ⇒ (x, y^(3/2)) . . . . . a non-linear transformation
These only transform one coordinate. Of course, different transforms or combinations can be used on the different coordinates.
__
The attachment shows the effect of each of these. The red figure is the original icosagon (20-gon). The blue figure shows the horizontal stretch of the first transformation. The green figure shows the diagonal stretch of the shear transformation. The purple figure shows the effect of a non-linear transformation.
x = ?????????????????
Answer:
4
Step-by-step explanation:
What is the equation of the line which passes through (-0.5,-5) and (2,5)
Answer:
by using distance formula
d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
by putting the values of coordinates
[tex]d=\sqrt{(2-(-0.5))^2+(5-(-5))^2}[/tex]
[tex]d=\sqrt{(2+0.5)^2+(5+5)^2}[/tex]
[tex]d=\sqrt{(2.5)^2+(10)^2}[/tex]
[tex]d=\sqrt{6.25+100}[/tex]
[tex]d=\sqrt{106.25}[/tex]
[tex]d=10.3[/tex]
Step-by-step explanation:
i hope this will help you :)
20. Evaluate:
(55.5 x 2) = 5 + 13-7
Answer: 111=11
Step-by-step explanation: PEMDAS
(55.5 times 2)=5+13-7
(111)=5+13-7
(111)=18-7
111=11
Abigail and Liza Work as carpenters for different companies Abigail earns $20 Per hour at her company and Liza Word for a total of 30 hours in together earned a total of 690 how many hours did Liza work last week?
This question was not properly written, hence it is incomplete. The complete question is written below:
Complete Question:
Abigail and Liza work as carpenters for different companies. Abigail earns $20 per hour at her company and Liza earns $25 per hour at her company. Last week, Abigail and Liza worked for a total of 30 hours and together earned a total of $690. How many hours did Liza work last week?
Answer:
Lisa worked for 18 hours last week
Step-by-step explanation:
Let the number of hours Abigail worked last week = A
Let the number of hours Liza worked last week = B
Abigail earns = $20 per hour at her company
Liza earns = $25 per hour at her company
A + B = 30 ........... Equation 1
B = 30 - A
20 × A + 25 × B = 690
20A + 25B = 690 ............... Equation 2
Substitute 30 - A for B in Equation 2
Hence, we have:
20A + 25(30 - A) = 690
20A + 750 - 25A = 690
Collect like terms
20A - 25A = 690 - 750
-5A = -60
A = -60/-5
A = 12
Since A represents the number of hours Abigail worked, Abigail worked for 12 hours last week.
Substitute 12 for A in Equation 1
A + B = 30
12 + B = 30
B = 30 - 12
B = 18
Since B represents the number of hours Liza worked, therefore, Liza worked for 18 hours last week.
find the solution set x^2+2x-15=0
Answer:
x = 3 or x = -5
Step-by-step explanation:
x² + 2x - 15 = 0
Factor left side of equation.
(x - 3)(x + 5) = 0
Set factors equal to 0
x - 3 = 0
x = 3
x + 5 = 0
x = -5
what is the solution for the inequality l2x-6l<4
Answer:
x < 5 or x > 1
Step-by-step explanation:
2x - 6 < 4
2x < 4 + 6
2x < 10
x < 10/2
x < 5
2x - 6 > - 4
2x > - 4 + 6
2x > 2
x > 2/2
x > 1