Answer:
a. 45
b. 176
c. 252
Step-by-step explanation:
First take into account the concept of combination and permutation:
In the permutation the order is important and it is signed as follows:
P (n, r) = n! / (n - r)!
In the combination the order is NOT important and is signed as follows:
C (n, r) = n! / r! (n - r)!
Now, to start with part a, which corresponds to a combination because the order here is not important. Thus
n = 10
r = 2
C (10, 2) = 10! / 2! * (10-2)! = 10! / (2! * 8!) = 45
There are 45 possible scenarios.
Part b, would also be a combination, defined as follows
n = 10
r <= 3
Therefore, several cases must be made:
C (10, 0) = 10! / 0! * (10-0)! = 10! / (0! * 10!) = 1
C (10, 1) = 10! / 1! * (10-1)! = 10! / (1! * 9!) = 10
C (10, 2) = 10! / 2! * (10-2)! = 10! / (2! * 8!) = 45
C (10, 3) = 10! / 3! * (10-3)! = 10! / (2! * 7!) = 120
The sum of all these scenarios would give us the number of possible total scenarios:
1 + 10 + 45 + 120 = 176 possible total scenarios.
part c, also corresponds to a combination, and to be equal it must be divided by two since the coin is thrown 10 times, it would be 10/2 = 5, that is our r = 5
Knowing this, the combination formula is applied:
C (10, 5) = 10! / 5! * (10-5)! = 10! / (2! * 5!) = 252
252 possible scenarios to be the same amount of heads and tails.
The scale on a map is 2 centimeters= 50 kilometres.Two rivers on a map are located 9.3 centimeters apart.What is The actual distance between the two rivers
Answer:
The actual distance between the two rivers is 232.5 kilometers.
Step-by-step explanation:
GIven:
The scale on a map is 2 centimeters= 50 kilometres.Two rivers on a map are located 9.3 centimeters apart.
Now, to find the actual distance between the two rivers.
Let the actual distance between the two rivers is [tex]x.[/tex]
The two rivers on the map is located apart of 9.3 centimeters.
According to the scale on the map is 2 centimeters = 50 kilometers.
So, 2 centimeters is equivalent to 50 kilometers.
Thus, 9.3 centimeters is equivalent to [tex]x.[/tex]
Now, to solve by using cross multiplication method:
[tex]\frac{2}{50} =\frac{9.3}{x}[/tex]
By cross multiplying we get:
[tex]2x=465[/tex]
Dividing both sides by 2 we get:
[tex]x=232.5\ kilometers.[/tex]
Therefore, the actual distance between the two rivers is 232.5 kilometers.
Which of the following is not true? Choose the correct answer below. A. The area in any normal distribution bounded by some score x is the same as the area bounded by the equivalent z-score in the standard normal distribution. B. A z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution. C. A z-score is an area under the normal curve. D. If values are converted to standard z-scores, then procedures for working with all normal distributions are the same as those for the standard normal distribution.
Using concepts of the normal distribution, it is found that the statement which is not true is:
C. A z-score is an area under the normal curve.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The standard normal distribution has [tex]\mu = 0, \sigma = 1[/tex]. The z-score converts any distribution a standard normal. It 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, which is the area under the normal curve.Thus, statement C is false, as the p-value is the area under the normal curve, not the z-score.
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An air force pilot is flying at a cruising altitude of 9000 feet and is forced to eject from her aircraft. The function h(t)=-16t+128t+900. Determine and state the vertex of h(t)
Answer:
(t, h(t)) = (4, 9256)
Step-by-step explanation:
We assume you intend the h(t) function to be ...
h(t) = -16t^2 +128t +9000
The equation can be written in vertex form as follows:
h(t) = -16(t^2 -8t) +9000
h(t) = -16(t^2 -8t +16) +9000 -(-16)(16) . . . . add and subtract -16(16) to complete the square
h(t) = -16(t -4)^2 +9256 . . . . . vertex form of the height function
The vertex of h(t) is (4, 9256), an altitude of 9256 feet after 4 seconds.
A restaurant charges an automatic gratuity of 18% on tables with more than 6 people. A party of 8 had a bill of p. Which expression can be used to find the total cost of the meal with the gratuity?
0.18p
0.82p
1.18p
18.00p
The expression 1.18p can be used to find the total cost of the meal with gratuity.
Step-by-step explanation:
Step 1:
If there are more than 6 people, the restaurant charges an automatic gratuity of 18%.
Since there are 8 people this charge will also be applied here.
If the bill amount is p and 18% of p is added, the options 0.18p and 0.82p cannot be the total cost of the meal.
Step 2:
We need to determine how much 18% is in terms of p.
18% of p [tex]= \frac{18}{100} (p) = 0.18p.[/tex]
So the total cost of the meal = Cost of the meal + Gratuity charges [tex]=p + 0.18p = 1.18p.[/tex]
So the total cost is the third option 1.18p.
Answer:
1.18
Step-by-step explanation:
You are renting a limousine that charges certain rates to visit each of the following cities. You need to visit each city once and you need to start in Athens and end in Athens. Use the "Brute Force" Algorithm to find the cheapest route to visit each city and return home again to Athens.
Answer:
The cheapest route to visit each city and return home again to Athens is:
A→B→C→D→A or A→D→C→B→A.
Step-by-step explanation:
The Algorithm of Brute Force
List of all possible routesCalculate the charge of each route found in Step 1Pick the route which has the cheapest route.Let Athens ⇒A , Buford ⇒B , Cuming ⇒ C , Dacula ⇒ D
There are 6 routes to visit each city and return home again to Athens.
Route 1: A→B→C→D→A = 70 + 25 + 30 + 60 = $185
Route 2: A→B→D→C→A = 70 + 70 + 30 + 50 = $220
Route 3: A→C→B→D→A = 50 + 25 + 70 + 60 = $205
Route 4: A→C→D→B→A = 50 + 30 + 70 + 70 = $220
Route 5: A→D→B→C→A = 60 + 70 + 25 + 50 = $205
Route 6: A→D→C→B→A = 60 + 30 + 25 + 70 = $185
By checking the previous routes:
The cheapest charge will be $185 and it will be for the route
A→B→C→D→A or A→D→C→B→A.
Find [g•h](x) and [h•g] (x) g(x)=2x h(x)=-10x-10
Answer:
-40x(x+1)
Step-by-step explanation:
Find [g•h](x) and [h•g] (x)
g(x)=2x
h(x)=-10x-10
[g•h](x) = 2x(-10x-10)= -20x^2-20x = -20x(x+1)
[h•g](x) = (-10x-10)2x= -10x(2x)-10(2x) = -20x^2-20x
[g•h](x) and [h•g] (x)
and means addition
-20x^2-20x + (-20x^2-20x)
-20x^2-20x-20x^2-20x
choose like terms
-20x^2-20x^2-20x-20x
-40x^2-40x
-40x(x+1)
somebody help me plzzzz plz
Which of the following is the solution to 7/(x+2) + 11/(x-5) = 7/(x+2)(x-5)?
10/9
9/10
-10/9
-9/10
Option A: [tex]\frac{10}{9}[/tex] is the solution of x
Explanation:
The given expression is [tex]\frac{7}{(x+2)}+\frac{11}{(x-5)}=\frac{7}{(x+2)(x-5)}[/tex]
We need to determine the value of x.
The value of x can be determined by solving the expression for x.
Taking LCM , we get,
[tex]\frac{7(x-5)+11(x+2)}{(x+2)(x-5)}=\frac{7}{(x+2)(x-5)}[/tex]
Since, the denominator is common for both sides of the equation, let us cancel the denominator.
Thus, we have,
[tex]7(x-5)+11(x+2)=7[/tex]
Multiplying the terms within the bracket, we get,
[tex]7x-35+11x+22=7[/tex]
Adding the like terms, we get,
[tex]18x-13=7[/tex]
Adding both sides of the equation by 13, we have,
[tex]18x=20[/tex]
Dividing both sides of the equation by 18,
[tex]x=\frac{20}{18}[/tex]
Simplifying, we get,
[tex]x=\frac{10}{9}[/tex]
Thus, the solution is [tex]\frac{10}{9}[/tex]
Therefore, Option A is the correct answer.
Answer:
a
Step-by-step explanation:
At December 31, bonds payable of $109,993,000 are outstanding. The bonds pay 12% interest every September 30 and mature in installments of $27,498,250 every September 30, beginning September 30, 2018.
Answer:
Explanation:
If 112% interest of bond amount = $27,498,250
∴ 100% principal amount = 27,498,250 X 100/112 = $24,552,008.93
10% bond interest = $24,552,008.93 X 0.10 = $2,455,200.89
Between October 2018 and August 2019, it amounts = $2,455,200.09 X 11 = $27,007,209.82
The amount accrued up to September 2019 = $(27,007,209.82 + 27,498,250) = $54,505,459.82
From October 2019 to August 2020, it will amount = $(27,007,209.82 + 54,505,459.82) = $81,512669.64
The amount accrued up to September 2020 = $(81,512,669.64 + 27,498,250) = $109,010,919.64
Find the indicated term of the given geometric sequence.
a = –5, r = –2, n = 3
Question 16 options:
–20
–41
10
40
Answer: the first option is correct.
Step-by-step explanation:
In a geometric sequence, each consecutive term differ by a common ratio, r.
The formula for determining the nth term of a geometric progression is expressed as
an = a1r^(n - 1)
Where
a1 represents the first term of the sequence.
r represents the common ratio.
n represents the number of terms.
From the information given,
a = - 5
r = - 2
n = 3
Therefore, the 3rd term, T3 is
T3 = - 5 × - 2^(3 - 1)
T3 = - 5 × - 2^2
T3 = - 5 × 4
T3 = - 20
Just answer what it asks in the picture PLEASE
m∠1 = 30° (by Vertical angle theorem)
m∠A = 80° (by Triangle sum theorem)
m∠D = 80° (by Triangle sum theorem)
The value of x is 7.5 and y is 9.
Solution:
∠ACB and ∠DCE are vertically opposite angles.
Vertical angle theorem:
If two lines are intersecting, then vertically opposite angles are congruent.
⇒ m∠DCE = m∠ACB
⇒ m∠1 = 30° (by Vertical angle theorem)
In triangle ACD,
Triangle sum property:
Sum of the interior angles of the triangle = 180°
⇒ m∠A + m∠C + m∠B = 180°
⇒ m∠A + 30° + 70° = 180°
⇒ m∠A + 100° = 180°
⇒ m∠A = 100° – 180°
⇒ m∠A = 80° (by Triangle sum theorem)
Similarly, m∠D = 80° (by Triangle sum theorem)
In ΔACD and ΔDCE,
All the angles are congruent, so ΔACD and ΔDCE are similar triangles.
In similar triangle corresponding sides are in the same ratio.
[tex]$\frac{9}{12}=\frac{x}{10}[/tex]
Do cross multiplication.
90 = 12x
7.5 = x
Now, to find y:
[tex]$\frac{9}{12}=\frac{6}{y}[/tex]
Do cross multiplication.
9y = 72
Divide by 9, we get
y = 8
Hence the value of x is 7.5 and y is 9.
An arc on a circle measures 295°. The measure of the central angle
Answer:
59/36π
Step-by-step explanation:
We know that an angle is measured in either degrees or radians and The arc's angle measurement, taken at the center of the circle the arc is part of, is measured in degrees (or radians)
Let's convert 90 degrees into radians
295° = 295 * π/180 = 59/36π
Given square ABCD, what is the length of AD?
Answer:
since it's a square, all sides are equal
therefore,
3x - 5 = x + 1
2x = 6
x = 3
sub x into AD, which is 3x-5
= 3(3) - 5
= 9 - 5
= 4
therefore AD is 4 units
Step-by-step explanation:
The length of AD in a square ABCD is equal to the length of any other side.
Without specific measurements given for any side, the length of AD cannot be determined.
Explanation:To find the length of segment AD in a square ABCD, we utilize the properties of a square where all sides are equal.
Therefore, if you know the length of any other side of the square, that would be the length of AD as well.
However, since the length of AB, BC, or CD is not provided in the question, there is insufficient information to determine the length of AD.
Without additional information, such as the length of one of the sides or a relationship that includes AD, it is impossible to provide a numerical answer.
If the question related to the string exercise is part of the information to be used, we would need to know the length of ED or BD to find AD, again, as they are all equal in a square.
For any real-world application like in the trilateration example, measuring actual dimensions would be necessary.
The height of a volleyball, h, in feet, is given by h = −16t2 + 11t + 5.5, where t is the number of seconds after it has been hit by a player. The top of the net is 7.3 feet above the floor. Does the volleyball travel high enough to clear the top of the net?
Answer:
It will travel high enough
Step-by-step explanation:
Find the vertex of the parabola:
x=-b/2a
x=-11/2(-16)
x=-11/-32
x=11/32
Plug x=11/32 into quadratic to get the y-coordinate:
h=-16(11/32)^2+11(11/32)+5.5
h=7.391
Since 7.391>7.3, the volleyball will travel high enough (aka. yes)
To determine if the volleyball clears the net, we calculate the maximum height using the vertex of the parabola from the quadratic equation representing the ball's trajectory. By finding the time at the vertex and substituting it back into the equation, we get the maximum height, which needs to be compared with the net's height.
Explanation:To determine whether the volleyball travels high enough to clear the net, we need to calculate the maximum height reached by the ball using the given quadratic equation h = −16t2 + 11t + 5.5. The maximum height will be at the vertex of the parabola represented by the quadratic function. The t-coordinate of the vertex can be found using the formula t = -b/2a, where a and b are the coefficients from the quadratic term and the linear term respectively.
For the given equation h = -16t2 + 11t + 5.5, a is -16 and b is 11. Thus,
Doing the calculation will reveal the maximum height of the volleyball. If this height is greater than 7.3 feet, the height of the net, then the volleyball clears the net.
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i desperate for help plz come help
Which of the following are ordered pairs for the equation y =x - 3?
(0,3) (-2,-1) (2,5)
(0,3) (2,1) (-2,-5)
(0,-3) (2,-1) (-2,-5)
(0,-3) (2,-1) (-2,5)
A satellite views the Earth at an angle of 20°. What is
the arc measure, x, that the satellite can see?
O 40°
O 80°
160°
0 320
Answer:
The answer is 160
Step-by-step explanation:
The value of x is (πr - 20).
What is the arc length of a circle?The arc length of a circle is the distance between two points on the curve of the circle.
We have,
The measure of an angle formed by two tangents outside the circle.
= Difference of the intercepted arc / 2 ______(1)
Now,
Larger arc = (2πr - x)
Small arc = x
Angle = 20
Substituting in (1).
20 = (2πr - x - x) / 2
40 = 2πr - 2x
20 = πr - x
x = πr - 20
Thus,
The value of x is (πr - 20).
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Ty has 5 goats and 19 carrots. He gives each goat the same number of carrots, and he uses as many carrots as he can. How many carrots does Ty give each goat? How many carrots are left?
Each goat gets 3 carrots.
After giving 3 carrots to each of the goat, 4 carrots are left with Ty in total.
Step-by-step explanation:
Here, the total number of carrots = 19
The total number of goats = 5
So, in the given condition:
19 is the DIVIDEND
5 is the DIVISOR
Now, dividing 19 by 5, we get:
19 = 5 x 3 + 4
Here, 3 = Quotient
4 = Remainder
So, by the given equation. we can say that:
Each goat gets 3 carrots.
After giving 3 carrots to each of the goat, 4 carrots are left with Ty in total.
-2x^(2)+10x=-14 complete the square
Step-by-step explanation:
[tex]-2x^2+10x=-14\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x^2}{-2}+\dfrac{10x}{-2}=\dfrac{-14}{-2}\\\\x^2-5x=7\qquad(a-b)^2=a^2-2ab+b^2\qquad(*)\\\\x^2-2(x)(2.5)=7\qquad\text{add}\ 2.5^2\ \text{to both sides}\\\\\underbrace{x^2-2(x)(2.5)+2.5^2}_{(*)}=7+2.5^2\\\\(x-2.5)^2=7+6.25\\\\(x-2.5)^2=13.25[/tex]
[tex]\text{If you want the solution, then:}\\\\(x-2.5)^2=13.25\iff x-2.5=\pm\sqrt{13.25}\\\\x-\dfrac{25}{10}=\pm\sqrt{\dfrac{1325}{100}}\\\\x-\dfrac{25}{10}=\pm\dfrac{\sqrt{1325}}{\sqrt{100}}\\\\x-\dfrac{25}{10}=\pm\dfrac{\sqrt{25\cdot53}}{10}\\\\x-\dfrac{25}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{53}}{10}\\\\x-\dfrac{25}{10}=\pm\dfrac{5\sqrt{53}}{10}\\\\x-\dfrac{5}{2}=\pm\dfrac{\sqrt{53}}{2}\qquad\text{add}\ \dfrac{5}{2}\ \text{to both sides}\\\\x=\dfrac{5}{2}\pm\dfrac{\sqrt{53}}{2}[/tex]
[tex]\huge\boxed{x=\dfrac{5\pm\sqrt{53}}{2}}[/tex]
You have an SRS of 23 observations from a large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 95% confidence interval for the mean of the population?
Answer:
Therefore the critical value= 2.073
Step-by-step explanation:
The number of observation = 23.
For the mean of the population the confidence interval = 95%.
Here mean and stander deviation of the distribution is not given. So we use t distribution.
T distribution is called as student's t distribution.
Sample number =n =23.
Confidence level = c= 95% =0.95
The degree of freedom is sample size decreased by 1
df=n-1 = 23-1 =22.
The critical value [tex]t^*[/tex] can be found in the row df = 22 and column with 0.95 of the T distribution table .
[tex]t^*[/tex] = 2.073
Therefore the critical value= 2.073
To calculate the critical value for a 95% confidence interval when the sample size is small (less than 30), we need to use the t-distribution. The critical value from the t-distribution will depend on the sample size (specifically, the degrees of freedom) and the desired level of confidence.
Here's how you could calculate this step by step without using the Python function mentioned:
**Step 1: Identify the desired confidence level.**
For a 95% confidence interval, we are interested in capturing the central 95% of the t-distribution.
**Step 2: Determine the degrees of freedom.**
The degrees of freedom (df) for a t-distribution is equal to the sample size minus 1. So with 23 observations, df = 23 - 1 = 22.
**Step 3: Find the critical t-value.**
We want to find the critical t-value for the t-distribution with 22 degrees of freedom that corresponds to the 95% confidence interval. This means we want to find the t-value such that 95% of the distribution lies between -t and +t. Because the t-distribution is symmetric, we can look up the critical value for 97.5% (to split the remaining 5% evenly on both tails of the distribution).
Using a t-distribution table (often found in the appendices of statistics textbooks) or a statistical computing resource, you would find the t-value that corresponds to a cumulative probability of 0.975 with 22 degrees of freedom.
**Step 4: Interpret the table or resource correctly.**
If you were looking at a table, you would look down the degrees of freedom column until you find 22, then right to the column that represents the 97.5% cumulative probability (remember, this is for the two-tailed test). That entry is the critical t-value that corresponds to a 95% confidence interval.
**Step 5: Use the critical t-value for constructing the interval.**
Once you have the critical t-value, you would use it to construct the confidence interval for the population mean by multiplying this t-value by the standard error of the sample mean and then add and subtract this value from the sample mean.
**Important Note:**
Please be aware that the exact t-value varies depending on the source of the statistical tables or the statistical software being used. The value also depends on the precision (number of decimals) presented in the table.
If you perform these steps with a standard statistical table or software, you should find that the critical t-value for a 95% confidence interval with 22 degrees of freedom is approximately 2.074.
Tony collected 16.2 pounds of pecans from the trees on his farm.He will give the same weight of pecans to each of 12 friends.How many pounds of pecans will each friend get.
Each friend will get 1.35 pounds of pecans.
To find this, simply divide 16.2 by 12 to find the weight of pecans everyone gets. Thus making 1.35 pounds of pecans the answer.
I hope this helps!
After years of practicing at the local bowling alley, Allan has determined that his distribution of bowling scores is roughly symmetric, unimodal, and bell-shaped, with a mean of 182 points and a standard deviation of 23 points. How likely is it that Allan will roll a perfect game (300 points), just by random chance?
Answer:
P(x = 300) = 1.45 × 10⁻⁷
Step-by-step explanation:
This is a normal distribution problem with mean number of points = μ = 182 points
Standard deviation = σ = 23 points
Probability that Allan will roll a perfect game (300 points), just by random chance.
First of, we need to normalize/standardize 300.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (300 - 182)/23 = 5.13
300 is 5.13 Standard deviation from the mean
Probability of scoring 300 points = P(x = 300) = P(z = 5.13)
Using the normal distribution formula which is presented in the attached image to this question,
The mean = μ = 182
Standard deviation = σ = 23
x = variable whose probability is required = 300
P(x = 300) = P(z = 5.13) = 1.449193 × 10⁻⁷
Extremely unlikely!
Hope this helps!!!
The growth of a local raccoon population approximates a geometric sequence where an is the number of raccoons in a given year and n is the year. after 6 years there are 45 raccoons and after 8 years there are 71 raccoons.
Answer:
GENERAL EXPLICIT SEQUENCE IS GIVEN [tex]a_n = (14.74)(r)^{n-1)}[/tex]
Step-by-step explanation:
Let n be the number of year the data is recorded in.
a: The number of raccoons taken initially.
r: The multiplying factor
[tex]a_n[/tex] : The number of raccoon in the nth year.
As given: [tex]a_6 = 45, a_8 = 71[/tex]
Now, as the given situation can be expressed as GEOMETRIC SERIES:
[tex]a_n = a r^{(n-1)}[/tex]
Applying the same to given terms, we get:
[tex]a_6 = a r^{(6-1)} = ar^5 = 45\\\implies ar^5 = 45[/tex]
[tex]a_8 = a r^{(8-1)} = ar^7 =71\\\implies ar^7 = 71[/tex]
Dividing both equations, we get:
[tex]\frac{ar^7}{ar^5} = \frac{71}{45} \\\implies r^2 = 1.58\\\implies r = 1.25[/tex]
So, the first term [tex]a = \frac{45}{(1.25)^5} = 14 .74 \approx 15[/tex]
So, the GENERAL EXPLICIT SEQUENCE IS GIVEN as: [tex]a_n = (14.74)(r)^{n-1)}[/tex]
plz help dont skip
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-2, 2) and point (4, 4) rounded to the nearest tenth?
4 units
5.7 units
1 unit
6.3 units
Answer:
The answer to your question is 6.3 units
Step-by-step explanation:
Data
A (-2, 2)
B (4, 4)
Distance = ?
Formula
dAB = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
Substitution
x1 = -2 x2 = 4 y1 = 2 y2 = 4
dAB = [tex]\sqrt{(4 + 2)^{2} + (4 - 2)^{2}}[/tex]
Simplification
dAB = [tex]\sqrt{6^{2} + 2^{2}}[/tex]
dAB = [tex]\sqrt{36 + 4}[/tex]
dAB = [tex]\sqrt{40}[/tex]
Result
dAB = 6.3 units
Factor the expression. d2 – 4d + 4
(d + 2)2
(d – 4)(d – 1)
(d – 2)2
(d – 2)(d + 2)
The expression d^2 - 4d + 4 factors to (d - 2)^2.
To factor the expression d^2 + 4d + 4, we are looking for two binomials that will multiply together to give us the original quadratic expression. These binomials will be of the form (d - a)^2 because the last term is a perfect square (4 = 22) and the middle term is twice the product of the square roots of the first and last terms.
Here's the step-by-step factoring:
1. Identify the square root of the first term, which is d.
2. Identify the square root of the last term, which is 2.
3. Since our middle term is negative, we use negative signs in our binomials.
4. The factored form is (d - 2)^2, as this will expand to d^2 - 2*d*2 + 22, which simplifies to d^2 - 4d + 4.
Madison Middle School has a math and science club that holds meetings after school. The club has decided to enter a two-day competition that involves different a math science challenges. The first day of competition involves solving multi-step math problems. Teams will receive two points for every problem they get correct in the morning session and three points for every question they get correct in the afternoon session.
a. Write an equation to represent the situation. Remember to define your variable(s)
b. The team scores four points in the morning session, but finishes the day with 28 points. Solve the equation and interpret the solution in the context of the problem.
c. The second day of the competition the science portion, involving hands-on science problems. Each correct science problem is worth 5 points. If the team started the day with 28 points and ended with 53 points, how many science problems did they get correct? Write and solve the an equation to answer the question.
Answer:
Please see attached picture for full solution.
Final answer:
The math and science club scored points by solving problems in a competition, with a total of 8 math problems solved on the first day and 5 science problems on the second day.
Explanation:
The situation from Madison Middle School's math and science club competition can be represented and solved with mathematical equations. Let's break down each part of the problem.
Part A: Equation Representation
Let m be the number of problems solved in the morning, and a the number in the afternoon. The equation representing the total points for the day is: 2m + 3a = Total Points.
Part B: Solving for the Afternoon Session
The team scored 4 points in the morning, meaning they solved 2 problems (as each is worth 2 points). This gives us the equation 2*2 + 3a = 28. Solving this, we find a = 8. Thus, the team solved 8 problems in the afternoon session to finish the day with 28 points.
Part C: Science Portion on the Second Day
On the second day, the team starts with 28 points and ends with 53 points, all from solving science problems worth 5 points each. The equation is 5s + 28 = 53, where s is the number of science problems solved. This simplifies to s = 5, indicating the team solved 5 science problems.
5. Solve for x in the equation 6x = 42.
A. x = 48
B. x = 7
- C.x=6
D. x = 36
Answer:
B. x= 7
Step-by-step explanation:
6x = 42
x = 42 / 6
x = 7
The 6 is multiplying because of the x, this passes to the other side of the equal to split.
Tarun has 4 more than the twice the number of tshirts Deepak has.Mahesh has 2 more than thrice the number of T-shirts that Tarun has.If the ratio is 6:7 find the number of T-shirts each of them has.
Answer:
Deepak: 4 t-shirts,
Tarun: 12 t-shirts,
Mahesh: 14 t-shirts.
Step-by-step explanation:
Let x represent number of t-shirts that Deepak has.
Please consider the complete question.
Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has. Mahesh has 2 more than thrice the number of T-shirts Deepak has. If the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, find out the number of the t-shirt each of them has.
Since Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has, so the number of t-shirts that Tarun has would be [tex]2x+4[/tex].
We are also told that Mahesh has 2 more than thrice the number of T-shirts Deepak has. So the number of t-shirts that Mahesh has would be [tex]3x+2[/tex].
Since the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, so we can represent this information in an equation as:
[tex]\frac{2x+4}{3x+2}=\frac{6}{7}[/tex]
Cross multiply:
[tex]6(3x+2)=7(2x+4)[/tex]
[tex]18x+12=14x+28[/tex]
[tex]18x-14x+12-12=14x-14x+28-12[/tex]
[tex]4x=16[/tex]
[tex]x=\frac{16}{4}=4[/tex]
Therefore, Deepak has 4 t-shirts.
The number of t-shirts that Tarun has would be [tex]2x+4\Rightarrow 2(4)+4=4+4=12[/tex]
Therefore, Tarun has 12 t-shirts.
The number of t-shirts that Mahesh has would be [tex]3x+2\Rightarrow 3(4)+2=12+2=14[/tex]
Therefore, Mahesh has 14 t-shirts.
Cara bought a DVD for $22 and a CD for less than the cost of the DVD let C represent the the cost of the CD write an inequality to show the cost of the CD
Answer:
C < 22
Step-by-step explanation:
dont skip help me plzzz will mark brainliest
Answer:
(6,-6)
Step-by-step explanation:
well if you count over to the right 6 and down 6 that points would be
(6,-6)
Answer:
(6,-6)
Step-by-step explanation:
The answer is that because the x-axis for A is positive and it is 6 points away from the origin. The y-axis for A should negative this is because the quadrants are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (x; y) coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −). The point is also 6 units away from the origin.
Henry is trapped at the roof top of a burning building, which is 24 feet high. In order to rescue him, his father, Diego, must find a ladder which will be used to cross the river, which is 7 feet wide, and go up directly to the top of the building. Help Diego to find the appropriate length of ladder from the other side of the river to the top of the building
Answer: the ladder should be 25 feet
Step-by-step explanation:
The ladder forms a right angle triangle with the building and the river. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.
The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.
To determine the length of the required ladder h, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
h² = 24² + 7² = 576 + 49
h² = 625
h = √625 = 25 feet
A rectangular public park has an area of 3,600 square feet. It is surrounded on three sides by a chain link fence. If the entire length of the fence measures 180 feet, how many feet long could the unfenced side of the rectangular park be?
Answer:
If length of the field is 30 ft, then width is 120 ft.
If the length of the field is 60 ft, then width is 60 ft.
Step-by-step explanation:
Let us assume the length of the rectangular park = L ft
Let us assume the breadth of the rectangular park = B ft
Now, AREA of the given park = L x B
⇒ L x B = 3,600 sq ft ... (1)
Also, the perimeter of three sides = 180 ft
⇒ 2 L + B = 180 ..... (2)
Now, from (1) and (2), we get:
L x B = 3,600
2 L + B = 180 ⇒ B = 180 - 2 L
Substitute this in(1) , we get:
L x B = 3,600 ⇒ L x (180 - 2 L) = 3600
[tex]\implies 180 L - 2L^2 = 3600\\\implies L^2 -90L + 1800 = 0\\\implies (L-30)(L-60)= 0[/tex]
⇒ L = 30 or L = 60
So, if L = 30 ft , then B = 180 - 2L = 180 - 60 = 120 ft
So, if L = 60 ft , then B = 180 - 2L = 180 - 120 = 60 ft
So, if length of the field is 30 ft, then width is 120 ft.
And if the length of the field is 60 ft, then width is 60 ft.