Answer:
six single scoops icecream cones
Question 15 A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 3 tables is $38 . The total cost to rent 2 chairs and 5 tables is $35 . What is the cost to rent each chair and each table?
Answer:
Each table is $6 and each chair is $2.50
Step-by-step explanation:
(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 a fashion company determines that the cost, in dollars, of producing x cellphone cases is given by C(x)equalsnegative 0.05 x squared plus 55 x. Find StartFraction Upper C (251 )minus Upper C (250 )Over 251 minus 250 EndFraction , and interpret the significance of this result to the company. StartFraction Upper C (251 )minus Upper C (250 )Over 251 minus 250 EndFraction equals nothing (Simplify your answer.) Interpret the significance of this result to the company. Choose the correct answer below. A. It represents the additional cost to produce one more item after making 250 items. B. It represents the additional cost to produce one item after the fixed costs have been paid. C. It represents the average cost per item to produce 250 items. D. It represents the average cost of producing 251 items.
Answer:
(a)$29.95
(b)A
Step-by-step explanation:
The cost, in dollars, of producing x cellphone cases is given by:
[tex]C(x)=-0.05 x^2+55 x.[/tex]
We are required to evaluate: [tex]\dfrac{C(251)-C(250)}{251-250}[/tex]
[tex]C(251)=-0.05(251)^2+55(251)=10654.95\\C(250)=-0.05(250)^2+55(250)=10625\\\text{Therefore:}\\\\\dfrac{10654.95-10625}{251-250}=29.95[/tex]
[tex]\dfrac{C(251)-C(250)}{251-250}=\$29.95[/tex]
The value calculated above represents the additional cost to produce one more item after making 250 items.
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
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
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
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.
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.
Use the information given to write an equation in standard form (If possible please show work)
Answer:
-2x + y = -1.
Step-by-step explanation:
The slope of the line = rise / run
= (11-9) / (6-5) = 2.
The point-slope form of the line is
y - y1 = 2(x - x1) where (x1, y1) is a point on the line so we have:
y - 11 = 2(x - 6) ( using the point (6, 11)
y = 2x - 12 + 11
y = 2x - 1
Convert to standard form:
-2x + y = -1.
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
If f(x) = 3x2 − 8x, 0 ≤ x ≤ 3, evaluate the Riemann sum with n = 6, taking the sample points to be right endpoints.
Split up the interval [0, 3] into 6 subintervals,
[0, 1/2], [1/2, 1], [1, 3/2], [3/2, 2], [2, 5/2], [5/2, 3]
The right endpoints are given by the arithmetic sequence,
[tex]r_i=0+\dfrac i2=\dfrac i2[/tex]
with [tex]1\le i\le6[/tex].
We approximate the integral of [tex]f(x)[/tex] on the interval [0, 3] by the Riemann sum,
[tex]\displaystyle\int_0^3f(x)\,\mathrm dx=\sum_{i=1}^6f(r_i)\Delta x_i[/tex]
[tex]\displaystyle=\frac{3-0}6\sum_{i=1}^6\left(3{r_i}^2-8r_i\right)[/tex]
[tex]\displaystyle=\frac12\sum_{i=1}^6\left(\frac{3i^2}4-4i\right)[/tex]
[tex]\displaystyle=\frac38\sum_{i=1}^6i^2-2\sum_{i=1}^6i[/tex]
Recall the formulas,
[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]
[tex]\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6[/tex]
Then the value of the integral is approximately
[tex]\displaystyle=\frac38\cdot\frac{6\cdot7\cdot13}6-2\cdot\frac{6\cdot7}2=\boxed{-\frac{63}8}=-7.875[/tex]
Compare to the exact value of the integral, -9.
The Riemann sum of [tex]f(x) = 3\cdot x^{2}-8\cdot x[/tex] with [tex]n = 6[/tex] is [tex]-\frac{63}{8}[/tex].
The formula for the right Riemann sum is described below:
[tex]S = \frac{b-a}{n} \cdot \Sigma\limit_{i= 1}^{n} \,f(x+i\cdot \frac{b-a}{n} )[/tex] (1)
Where:
[tex]S[/tex] - Riemann sum.[tex]a[/tex] - Lower bound.[tex]b[/tex] - Upper bound.[tex]n[/tex] - Number of segments.[tex]i[/tex] - Segment index.If we know that [tex]f(x) = 3\cdot x^{2}-8\cdot x[/tex], [tex]a = 0[/tex], [tex]b = 3[/tex] and [tex]n = 6[/tex], then the Riemann sum is:
[tex]S = \frac{3-0}{6}\cdot [f(0.5) + f(1) + f(1.5) + f(2) + f(2.5) +f(3)][/tex]
[tex]S = \frac{1}{2}\cdot \left(-\frac{13}{4}-5-\frac{21}{4}-4-\frac{5}{4}+3\right)[/tex]
[tex]S = -\frac{63}{8}[/tex]
The Riemann sum of [tex]f(x) = 3\cdot x^{2}-8\cdot x[/tex] with [tex]n = 6[/tex] is [tex]-\frac{63}{8}[/tex].
We kindly invite to check this question on Riemann sum: https://brainly.com/question/23960718
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
¿Qué hora es? Si el cuadrado de la mitad del
número de horas que faltan transcurrir del día,
coinciden con el número de horas transcurridas
del día.
Answer:
Si el cuadrado de la mitad del número de horas que faltan transcurrir del día coinciden con el número de horas transcurridas del día, son las 16:00 hs.
Step-by-step explanation:
Si el cuadrado de la mitad del número de horas que faltan transcurrir del día coinciden con el número de horas transcurridas del día, son las 16:00 hs.
Esto es así porque, como primera medida, la mitad de horas que faltan transcurrir del día no puede ser mayor a 4, puesto que 5 al cuadrado da como resultado 25, es decir, excede el número de horas que tiene un día.
Entonces, siguiendo con dicho razonamiento en sentido decreciente, tenemos que 4 al cuadrado da como resultado 16 (4 x 4). En este caso, 4 sería la mitad de horas que faltan transcurrir en el día, y 16 las horas ya transcurridas. Entonces, como 16 mas 8 da 24, y esa es la cantidad de horas que tiene el día, ésta es la opción correcta.
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 :)
What the sum for (50+11)*(8p-4)
Answer:
488p - 244
Step-by-step explanation:
Step 1: Add
61(8p - 4)
Step 2: Distribute
488p - 244
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2 days. What is the probability of spending between 4 and 7 days in recovery? (Round your answer to four decimal places.)
Answer:
The probability of spending between 4 and 7 days in recovery
P(4≤x≤7) = 0.5445
Step-by-step explanation:
Step(i):-
Given mean of the Population μ = 5.3 days
Given standard deviation of the population 'σ' = 2 days
Let 'X' be the random variable in normal distribution
Let x₁ = 4
[tex]Z_{1} = \frac{x_{1}-mean }{S.D} = \frac{4-5.3}{2} = -0.65[/tex]
Let x₂ = 7
[tex]Z_{2} = \frac{x_{2}-mean }{S.D} = \frac{7-5.3}{2} = 0.85[/tex]
Step(ii):-
The probability of spending between 4 and 7 days in recovery
P(4≤x≤7) = P(-0.65≤Z≤0.85)
= P(Z≤0.85) - P(Z≤-0.65)
= 0.5 + A( 0.85) - ( 0.5 - A(-0.65)
= 0.5 + A( 0.85) - 0.5 +A(0.65) ( ∵A(-0.65) = A(0.65)
= A(0.85) + A(0.65)
= 0.3023 + 0.2422
= 0.5445
Final answer:-
The probability of spending between 4 and 7 days in recovery
P(4≤x≤7) = 0.5445
The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. What are the minimum value of the bill that is greater than 95% of the bills?
Answer:
The minimum value of the bill that is greater than 95% of the bills is $37.87.
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 28, \sigma = 6[/tex]
What are the minimum value of the bill that is greater than 95% of the bills?
This is the 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 28}{6}[/tex]
[tex]X - 28 = 6*1.645[/tex]
[tex]X = 37.87[/tex]
The minimum value of the bill that is greater than 95% of the bills is $37.87.
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%
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
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!!!
PLZ HELP ME!!! Which of the following equations has both -6 and 6 as possible values of c? Choose all that apply A. c^2=36 B. c^3=216 C. None Of The Above
Let's solve the first equation and see if both -6−6minus, 6 and 666 are possible values of ccc.
Hint #22 / 4
\begin{aligned} c^2&=36\\\\ \sqrt{c^2}&=\sqrt{36}&\\\\ c &=\pm 6 \end{aligned}
c
2
c
2
c
=36
=
36
=±6
Yes, both -6−6minus, 6 and 666 are possible values of ccc for the first equation!
Hint #33 / 4
Let's do the same for the second equation.
\begin{aligned} c^3&=216\\\\ \sqrt[\scriptstyle 3]{c^3}&=\sqrt[\scriptstyle 3]{216}&\\\\ c &=6 \end{aligned}
c
3
3
c
3
c
=216
=
3
216
=6
No, both -6−6minus, 6 and 666 are not possible values of ccc for the second equation.
Hint #44 / 4
The following equation has both -6−6minus, 6 and 666 as possible values of ccc:
c^2 = 36c
2
=36
The equation that has both -6 and 6 as possible values is c² = 36.
Option A is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
If c is a possible value of 6, then c - 6 = 0.
Similarly, if c is a possible value of -6, then c + 6 = 0.
A)
c² = 36
We can factor this equation as c² - 36 = 0, which gives us (c - 6) (c + 6) = 0. Therefore, both c = 6 and c = -6 are solutions to this equation.
B)
c³ = 216
We can factor 216 as 6³, so c³ - 6³ = (c - 6) (c² + 6c + 36) = 0.
The quadratic factor c² + 6c + 36 does not have any real roots, so the only solution to this equation is c = 6.
Therefore, -6 is not a possible solution to this equation.
Thus,
The equation that has both -6 and 6 as possible values is c² = 36.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ3
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.
For the functions f(x)=3x−1 and g(x)=4x−3, find (f∘g)(x) and (g∘f)(x)
solve for z.
z/12 < 3
Answer: z < 36
Step-by-step explanation: To solve for z in this inequality, we multiply by 12 on both sides of the inequality to get z < 36.
We can write this in set notation as {z: z < 36}.
━━━━━━━☆☆━━━━━━━
▹ Answer
z < 36
▹ Step-by-Step Explanation
[tex]\frac{z}{12} < 3\\\\12 * \frac{z}{12} < 12 * 3\\\\z < 12 * 3\\\\z < 36[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
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!
A survey was conducted to find out how many people use public transportation to get to work. The results for 4625 respondents are broken down by gender: 1000 of 2570 males and 1532 of 2055 females use public transportation every working day. Use the information to find the standard error for the difference in proportions of males and females who use public transportation every working day and check the conditions for a normal distribution.
Answer:
The standard error for the difference in proportions of males and females who use public transportation every working day is 0.015.
The conditions are met.
Step-by-step explanation:
The sample 1 (males), of size n1=2570 has a proportion of p1=0.389.
[tex]p_1=X_1/n_1=1000/2570=0.389[/tex]
The sample 2 (females), of size n2=2055 has a proportion of p2=0.745.
[tex]p_2=X_2/n_2=1532/2055=0.745[/tex]
The difference between proportions is (p1-p2)=-0.356.
[tex]p_d=p_1-p_2=0.389-0.745=-0.356[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{1000+1532}{2570+2055}=\dfrac{2532}{4625}=0.547[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.547*0.453}{2570}+\dfrac{0.547*0.453}{2055}}\\\\\\s_{p1-p2}=\sqrt{0.000096+0.000121}=\sqrt{0.000217}=0.015[/tex]
Conditions for a normal distribution approximation:
The expected number of "failures" or "successes", whichever is smaller, has to be larger than 10.
For the males sample, we have p=0.389 and (1-p)=0.611. The sample size is n=2570, so we take the smallest proportion and chek the condition:
[tex]n\cdot p=2570\cdot 0.389=999>10[/tex]
For the females sample, we have p=0.745 and (1-p)=0.255. The sample size is n=2055, so we take the smallest proportion and chek the condition:
[tex]n\cdot (1-p)=2055\cdot 0.255=524>10[/tex]
The conditions are met.
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
Identify all the central angles
Answer:
Option 4
Step-by-step explanation:
The central angles are "Angles in the center"
So,
Central Angles are <AOB, <BOC and <AOC
Answer:
<AOB, <BOC and < AOC
Step-by-step explanation:
There are 3 angles at center O . The largest is <AOC ( = 180 degrees). Thn you have 2 more each equal to 90 degrees.
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]
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.