Step-by-step explanation:
x²+12x=40
(x+6)²-6²-40=0
(x+6)²-76 = 0
Tory and Emilio's motorboats travel at the same speed Tory pilots her boat 60 km before docking Emilio continues for another 4 hr traveling a total of 120 km before docking How long did it take Tory to navigate the 60 km?
It took Tory hr to navigate the 60 km
(Simplify your answer. Type an integer, a mixed numeral or a fraction)
Answer:
2 hours
Step-by-step explanation:
Since Tory and Emilio's motorboats travel at the same speed, they are traveling at the speed of 30 km/h. Therefore, it should take Tory two hours to travel 60 km.
Tory took 2 hours to navigate the 60 kilometers.
What is speed?Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.
Given:
Tory pilots her boat 60 km before docking.
Emilio continues for another 4 hours traveling, a total of 120 km before docking.
The speed of Emilio's boat = 120 / 4 = 30 kilometers per hour.
Tory and Emilio's motorboats travel at the same speed.
Tory's boat speed,
= 60/30 = 2 hours.
Therefore, Tory takes 2 hours.
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Please explain absolute values?
Answer:
the magnitude of a real number without regard to its sign.
Step-by-step explanation:
For example, |-3| would just be a 3 in general, no negative sign in the front.
hope this answers your confusion.
Find the area of the regular pentagon. 4.1 cm 6 cm Area = [?] cm? Enter your answer to the nearest tenth.
Answer:
Area of the given regular pentagon is 61.5 cm².
Step-by-step explanation:
Area of a regular polygon is given by,
Area = [tex]\frac{1}{2}aP[/tex]
Here, a = Apothem of the polygon
P = Perimeter of the polygon
Apothem of the regular pentagon given as 4.1 cm.
Side of the pentagon = 6 cm
Perimeter of the pentagon = 5(6)
= 30 cm
Substituting these values in the formula,
Area = [tex]\frac{1}{2}(4.1)(30)[/tex]
= 61.5 cm²
Therefore, area of the given regular pentagon is 61.5 cm².
Can someone please answer this
Answer:
Tisco: 12 for £5.16
Azda: 12 for £5.04
Azda has the better value.
Step-by-step explanation:
Tisco: 3 for £1.29
Multiply both numbers by 4.
12 for £5.16
Azda:
4 for £1.68
Multiply both numbers by 3.
12 for £5.04
Azda has the better value.
The accompanying data represent the homework scores for material for a random sample of students in a college algebra course.
36
47
54
58
60
66
66
68
69
70
72
75
77
77
78
78
78
79
79
79
79
79
80
82
84
85
86
86
86
87
89
89
91
92
92
93
93
94
96
99
(a) Construct a relative frequency distribution with a lower class limit of the first class equal to 30 and a class width of 10.
(b) What is the probability a randomly selected student fails the homework (scores less than 70)? (The standard deviation is 13.64)
Simplify your answer to two decimal places.
Answer:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]
[tex]P(x < 70) = 0.225[/tex]
Step-by-step explanation:
Given
[tex]Lower = 30[/tex]
[tex]Width = 10[/tex]
Solving (a): The relative frequency table
First, we construct the frequency table using the given parameters.
[tex]\begin{array}{cc}{Class} & {Frequency} &{30-39} & {1} & {40-49} & {1} & {50 - 59} & {2} & {60 - 69} & {5} & {70 - 79} & {13} & {80 - 89} & {10} & {90 - 99} & {8} & {Total} & {40}\ \end{array}[/tex]
The relative frequency (RF) is calculated as:
[tex]RF = \frac{Frequency}{Total}[/tex]
Using the above formula to calculate the relative frequency, the relative frequency table is:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]
Solving (b): [tex]P(x < 70)[/tex]
To do this, we add up the relative frequencies of classes less than 70.
i.e.
[tex]P(x < 70) = [30 - 39] + [40 - 49] + [50 - 59] + [60 - 69][/tex]
So, we have:
[tex]P(x < 70) = 0.025 + 0.025 + 0.050 + 0.125[/tex]
[tex]P(x < 70) = 0.225[/tex]
To add radical expressions, the expressions must have the same index and radicand,
True
False
URGENT PLS HELP
Given f(y)=2y^2 - 4y, and h(x)= x^2 - 1, determine f(h(x))
Answer:
f(h(x)) = 2•(x²-1)² -4•(x²-1)
A decorative wall in a garden is to be build using bricks that are 3 3/4 inches thick and mortar joints that are 1/4 inch. Use the diagram to find the height of the wall
Step-by-step explanation:
we cannot see the diagram, so we don't know how many layers of bricks are used. and therefore it is impossible to tell the height of the wall.
the number of cases of a new diease can be modeled by the quadratic
Step-by-step explanation:
The number of cases of a new disease may be modeled by the quadratic regression equation y=-2x^2+44x+8 , what is the best prediction for the number of cases after 20 years ( the carrot symbol (^) means the following number is the exponent)
A professor creates a histogram of test scores for 26 students in a statistics course. What is the probability of a student having scored between 65 and 100
Complete Question
Complete is Attached Below
Answer:
Option D
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=26[/tex]
Student scoring [tex]65-100 n'=12[/tex]
Generally the equation for probability of a student having score between 65 and 100 is mathematically given by
[tex]P(65-100)=\frac{12}{26}[/tex]
[tex]P(65-100)=12/26[/tex]
[tex]P(65-100)=0.462[/tex]
Option D
Please explain the misleading
There are more compact cars (4*10 = 40) compared to trucks (2*10 = 20); however, the pictogram might make it appear that there are more trucks because the individual truck icon is larger compared to an individual compact car icon.
To anyone giving this image a quick glance, they may erroneously conclude that there are more trucks since their eye would notice the trucks first. Also, the person might think there are more trucks because bigger sizes tend to correspond to more proportion.
In real life, a truck is larger than a compact car, but the icons need to be the same size to have the figure not be misleading.
A very similar issue happens with the mid-size cars vs the compact cars as well. The three mid-size car icons span the same total width as the compact cars do, indicating that a reader might mistakenly conclude that there are the same number of mid-size cars compared to compact ones (when that's not true either).
Please help me quick I’ll give brainliest
PLEASE HELP ASAP! So the answer I got for this problem is 50.26. Can someone make sure that is the correct answer? Please let me know how to solve this problem if it is wrong.
Answer:
Step-by-step explanation:
every thing looks good, except the question says "round" and soooooo, if you are rounding to the 2nd decimal place, then the next two decimal places are 54, or 50.2654 so, to round that, round up , so your final answer would look like 50.27 :) see?
9514 1404 393
Answer:
50.24 inches (or 50.2 inches)
Step-by-step explanation:
The formula for circumference in terms of radius is ...
C = 2πr
Using the given values for radius and for pi, the circumference is ...
C = 2(3.14)(8 in) = 50.24 in
__
Additional comment
If you use a more accurate value of pi, the rounded value is 50.27 in. That is not the value requested by this problem. It helps to follow directions.
If you like, you can round to 50.2, since only one decimal place is required in the result.
2.7.2 : Checkup - Practice Problems
A, B and C are collinear points. B is between A and C. AB=12 BC=18 AC=3x Find X.
Answer:
[tex]x =10[/tex]
Step-by-step explanation:
Given
[tex]AB = 12[/tex]
[tex]BC = 18[/tex]
[tex]AC = 3x[/tex]
Required
Solve for x
Since B is in between both points, then:
[tex]AC = AB + BC[/tex]
This gives
[tex]3x = 12 + 18[/tex]
[tex]3x = 30[/tex]
Divide by 3
[tex]x =10[/tex]
How high up the wall can a 12-foot ladder reach if its base is 4 feet from the wall? Round your answer to the nearest tenth of a foot if necessary.
Answer: 24 ft I think
Step-by-step explanation:
How to solve this problem what do I do
=================================================
Explanation:
We undo the "minus 6" by adding 6 to both sides.
Also, we undo the "+s" by subtracting s from both sides
-----------
So we have these steps
P = r+s-6
P+6 = r+s-6+6 .... adding 6 to both sides
P+6 = r+s
r+s = P+6
r+s-s = P+6-s ..... subtracting s from both sides
r = P + 6 - s
Answer:
P+6-s=r
Step-by-step explanation:
Hi there!
We are given the equation P=r+s-6 and we need to solve for r
To do that, we need to isolate r onto one side, and have everything else on the other.
Here is the equation:
P=r+s-6
start by adding 6 to both sides to clear it from the right side
P+6=r+s
now subtract s from both sides to clear it from the right side
P+6-s=r
now everything that isn't r is on the left side, and r is by itself on the right side. P+6-s=r is the answer.
Hope this helps!
Given n(A) = 1300, n(A U B) = 2290, and n(A n B) = 360, find n(B).
Answer:
n(B) = 1350
Step-by-step explanation:
Using Venn sets, we have that:
[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)[/tex]
Three values are given in the exercise.
The other is n(B), which we have to find. So
[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)[/tex]
[tex]2290 = 1300 + n(B) - 360[/tex]
[tex]940 + n(B) = 2290[/tex]
[tex]n(B) = 2290 - 940 = 1350[/tex]
So
n(B) = 1350
Round 36.319 to the nearest tenth
Express these system specifications using the propositions p “The user enters
a valid password,” q “Access is granted,” and r “The user has paid the
subscription fee” and logical connectives (including negations).
a) “The user has paid the subscription fee, but does not enter a valid
password.”
b) “Access is granted whenever the user has paid the subscription fee and
enters a valid password.”
c) “Access is denied if the user has not paid the subscription fee.”
d) “If the user has not entered a valid password but has paid the subscription
fee, then access is granted.”
Answer:
a) r ⋀~p
b)(r⋀p)⟶q
c) ~r ⟶ ~q
d) (~p ⋀r) ⟶q
Step-by-step explanation:
To solve this question we will make use of logic symbols in truth table.
We are told that;
p means "The user enters
a valid password,”
q means “Access is granted,”
r means “The user has paid the
subscription fee”
A) The user has paid the subscription fee, but does not enter a valid
password.”
Fist part of the statement is correct and so it will be "r". Second part of the statement is a negation and will be denoted by ~p. Since both statements are joined together in conjunction, we will use the conjuction symbol in between them which is "⋀" Thus, we have; r ⋀~p
B) Still using logic symbols, we have;
(r⋀p)⟶q
⟶ means q is true when r and p are true.
C) correct symbol is ~r ⟶ ~q
Since both statements are negation of the question. And also, if ~r is true then ~q is also true.
D) Similar to answer A to C above, applying similar conditions, we have (~p ⋀r) ⟶q
Unit sales for new product ABC have varied in the first seven months of this year as follows: Month Jan Feb Mar Apr May Jun Jul Unit Sales 148 329 491 167 228 285 441 What is the (population) standard deviation of the data
Answer:
[tex]\sigma = 121.53[/tex]
Step-by-step explanation:
Required
The population standard deviation
First, calculate the population mean
[tex]\mu = \frac{\sum x}{n}[/tex]
This gives:
[tex]\mu = \frac{148+ 329+ 491 +167+ 228+285+ 441}{7}[/tex]
[tex]\mu = \frac{2089}{7}[/tex]
[tex]\mu = 298.43[/tex]
The population standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{(148 - 298.43)^2 + ..........+ (441- 298.43)^2}{7}}[/tex]
[tex]\sigma = \sqrt{\frac{103387.7143}{7}}[/tex]
[tex]\sigma = \sqrt{14769.6734714}[/tex]
[tex]\sigma = 121.53[/tex]
Write the slope intercept form of the equation of each line.
1) The line through the point (4,2) and parallel to y+ -3/4x-5
Answer:
[tex]y = -\frac{3}{4}x + 5[/tex]
Step-by-step explanation:
Given equation y = -3/4x - 5
Step 1 : Find slope.
Since the lines are parallel to each other, the slopes are same.
[tex]therefore, m = \frac{-3}{4}[/tex]
Step 2 : Find the equation of the line.
[tex]( y - y_1) = m ( x - x_ 1) \ \ \ where \ x_ 1 = 4 \ and \ y_ 1 = 2[/tex]
[tex]( y - 2 ) = -\frac{3}{4}( x - 4)\\\\y - 2 = -\frac{3}{4}x + 3\\\\y = -\frac{3}{4}x + 3 + 2\\\\y = -\frac{3}{4}x + 5[/tex]
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. text({)1, 1/4, 1/16, 1/64, 1/256, ... text(})
Answer:
[tex]T_n = \frac{1}{4^{n-1}}[/tex]
Step-by-step explanation:
Given
[tex]({)1, 1/4, 1/16, 1/64, 1/256, ... (})[/tex]
Required
The general term
The given sequence is geometric.
So first, we calculate the common ratio (r)
[tex]r = T_2/T_1[/tex]
So, we have:
[tex]r = 1/4 \div 1[/tex]
[tex]r = 1/4[/tex]
The function is then calculated using:
[tex]T_n =T_1 * r^{n-1}[/tex]
This gives
[tex]T_n =1 * 1/4^{n-1}[/tex]
[tex]T_n = \frac{1}{4^{n-1}}[/tex]
As of 2012, the proportion of students who use a MacBook as their primary computer is 0.4. You believe that at your university the proportion is actually less than 0.4. If you conduct a hypothesis test, what will the null and alternative hypotheses be
Answer:
The null hypothesis is [tex]H_0: p = 0.4[/tex]
The alternative hypothesis is [tex]H_a: p < 0.4[/tex]
Step-by-step explanation:
As of 2012, the proportion of students who use a MacBook as their primary computer is 0.4.
At the null hypothesis, we test if the proportion is of 0.4, that is:
[tex]H_0: p = 0.4[/tex]
You believe that at your university the proportion is actually less than 0.4.
This means that at the alternative hypothesis, we test if the proportion is less than 0.4, that is:
[tex]H_a: p < 0.4[/tex]
Help me with moth of these questions please
Answer:
10. CD + DE = CE
11. BC + CE = BE
Step-by-step explanation:
10. CD and DE lie on a straight line, therefore, CD + DE = CE based on the segment addition postulate.
11. BC and CE lie on a straight line, therefore, BC + CE = BE based on the segment addition postulate.
Which of the following expressions would represent a class of 42 students divided equally into 7 groups?
Answer: [tex]7\sqrt{42}[/tex]
Step-by-step explanation:
42 students divided equally into 7 groups means 42 divided by 7, and [tex]7\sqrt{42}[/tex] is the only choice that shows that.
7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
A class of forty two Forty two students divided equally into 7 groups.
Forty two students divided equally into seven groups means forty two divided by seven, and
this can be done by using 7√42.
42 students divided equally into 7 groups means forty two divided by seven
Hence 7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
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Which graph represents the function?
Answer:
D
Step-by-step explanation:
I have attached the explanation above. hopefully this will help
What is the smallest three-digit number that is divisible by 3? Explain how you know without multiplying or dividing.
A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.
Answer:
[tex]E(x) = 1.5\\[/tex]
Step-by-step explanation:
Given
[tex]n = 9[/tex] -- number of rolls
Required
The mean of 2's
The distribution follows binomial distribution where:
[tex]X \to Binomial(n,p)[/tex]
In this case:
[tex]p= \frac{1}{6}[/tex] ---- the theoretical probability of rolling 2
So, the mean of 2's is calculated using:
[tex]E(x) = np[/tex]
[tex]E(x) = 9 * \frac{1}{6}[/tex]
[tex]E(x) = \frac{9}{6}[/tex]
Simplify
[tex]E(x) = \frac{3}{2}[/tex] or
[tex]E(x) = 1.5\\[/tex]
We have just performed a one-way ANOVA on a given set of data and rejected the null hypothesis for the ANOVA F test. Assume that we are able to perform a randomized block design ANOVA on the same data. For the randomized block design ANOVA, the null hypothesis for equal treatments will ________ be rejected.
Answer:
The answer is "sometimes".
Step-by-step explanation:
A one-way ANOVA was merely performed on one collected data and the null hypothesis was rejected after an ANOVA F test. Assume we could randomize ANOVA block design with the same information. This null hypothesis for full equality is sometimes rejected for the randomized complete block design ANOVA. Therefore we understand the use of randomized ANOVA block if the null hypothesis is denied of a one-way ANOVA but the rejection of a null RBD ANOVA hypothesis isn't conditional mostly on denial of the yet another ANOVA null.
