1. If Alex runs a mile in under 6 minutes, then he will have a new personal record. Alex ran a mile in 5 minutes and 45 seconds. Therefore, Alex set a new personal record. - law of Detachment
2. If you go to the water park, then you will need to bring sunscreen. If you do not bring sun screen, then you will burn. Therefore, when you go to the water park you will get a sunburn. - law of contrapositive
3. If two lines are parallel, then they never intersect. Line a and line b intersect. Therefore, line a and line b are not parallel - Law of Syllogism
4. If the measures of two angles in a triangle are 30° and 60°, then the third angle is 90°. If a triangle has a 90° angle, then it is a right triangle. Therefore, if a triangle has two angles that measure 30° and 60°, then it is a right triangle. - Not a valid conclusion
How to illustrate the information?According to the law of contrapositive, the initial assertion is accurate if and only if the contrapositive is accurate. The original assertion is untrue if the contrapositive is false. A conditional assertion that may or may not depend on another is a contrapositive.
Using deductive reasoning, a syllogism is a three-part logical argument in which two premises are joined to get a conclusion.
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Let y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that x and y are related by the equation y = 1100 + 15x.Answer the questions below.What is the change in the total cost for each book printed?What is the cost to get started (before any books are printed)?
y = 1100 + 15x.
Rewriting
y = 15x+1100
This is in slope intercept form
15 is the slope. It is the change for each x
It is the change for each book
The change in total cost for each book is 15 dollars
The y intercept is 1100. It is the cost when x =0. It is the cost when there are no books printed.
It is the cost to get started
The start up cost is 1100 dollars.
Jan made a mixed vegetable soup using tomatoes and carrots. Forty percent of the
tomatoes. If she used a total of 50 tomatoes, how many carrots should she use?
Jan should use 75 carrots for mixed vegetable soup.
Let us assume the total number of tomatoes and carrots be x. So, as per the mentioned information, the equation will be -
40%×x = 50
Converting percentage to fraction
40/100×x = 50
x = 50×100/40
Cancelling zero and performing division
x = 5×25
Performing multiplication
x = 125
Total number of vegetables = number of tomatoes + number of carrots
125 = 50 + Number of carrots
Number of carrots = 125 - 50
Performing subtraction
Number of carrots = 75
Therefore, Jan should use 75 carrots.
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The complete question is -
Jan made a mixed vegetable soup using tomatoes and carrots. Forty percent of the mixed vegetables were tomatoes. If she used a total of 50 tomatoes, how many carrots should she use?
Answer:
Step-by-step explanation:
75 carrots should be used
If the product of the extremes is 8,then the geometric mean is..
A. 2
B. 4
C. 2/2
Answer: THE ANSWER TO THAT IS C
Step-by-step explanation:
3b(u - 8) - n(u – 8) =
Answer:
3bu - 24b -nu + 8n
Step-by-step explanation:
Expanded
Add 7 3/10 simlify the answer and write it as a mixed number ?17/3011 7/2511 7/3011 17/30
To add mixed numbers first, we can add the whole numbers:
[tex]7+4=11[/tex]Now, we can add the fractions. For this, we can find the lowest common denominator (LCD) of both denominators. The LCD is the lowest number that is evenly divisible by both numbers. Since the denominators of the fractions are 10 and 15, the LCD is 30 because 30 is the smallest number that is divisible by 10 and 15. Then, we have:
[tex]\begin{gathered} \frac{3}{10}+\frac{4}{15}=\frac{3\cdot3}{10\cdot3}+\frac{4\cdot2}{15\cdot2} \\ \frac{3}{10}+\frac{4}{15}=\frac{9}{30}+\frac{8}{30} \\ \frac{3}{10}+\frac{4}{15}=\frac{9+8}{30} \\ \frac{3}{10}+\frac{4}{15}=\frac{17}{30} \end{gathered}[/tex]Therefore, the result of adding the given mixed numbers is:
[tex]$$\boldsymbol{7\frac{3}{10}+4\frac{4}{15}=11\frac{17}{30}}$$[/tex]A packet of carrot seeds has a germination rate of 92%. In other words, the probability of any
seed sprouting is 0.92. How many seedlings would you expect in a row of 50 seeds?
The number of constructive seedlings in a row of 50 seeds is 46.
What is probability of a given event and how can it be analyzed?
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability generally refers to the degree to which something is likely to occur. Utilize probability to ascertain how likely something is to occur. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty. Every event's probability in a sample space is one.
Given, the germination rate of the seeds to seedlings is = 92%
Therefore, the probability of any seed sprouting is 0.92.
Hence the required number of seedlings can be expected in a row of 50 seeds = 50*0.92 = 46 seeds
Thus, the number of constructive seedlings in a row of 50 seeds is 46.
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Identify the independent and dependent variables
the amount of gasoline in a car's fuel tank and the amount of time spent driving
Answer:
The independent variable is the time spent drive and the dependent variable with the amount of gas in the tank
Step-by-step explanation:
Does the gas in the tank depend on the time driving or does the time driving depend on the amount of gas in the car.
The amount of gas is the tank is determined by how much time the car is driven.
How to do because I dont know need help ASAP 20 points
Some arithmetic sequences could be easier to write as functions. As long as I know what value "n" has, I can find out any term in a particular Sequence whenever I need to. You might choose the implicit term over the prior term of a Sequence if it is known.
What is meant by Arithmetic Sequences?The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values.
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Some arithmetic sequences could be easier to write as functions. You are aware of the prior term.
Consider that we only have the numbers (...,4,...) from an arithmetic sequence with a common difference of 5.
The complete question is:
You are given the first four terms of an arithmetic sequence. Under what conditions might a recursive formula be preferred over the explicit formula? Under what conditions might an explicit formula be preferred over the recursive formula?
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A recipe for 2 dozen whole-wheat requires 600g of flour. How many muffins can be made with 900g of flour?
when we have a proportion it is defined as
[tex]\frac{a}{b}=k\cdot\frac{c}{d}[/tex]what this means is that we have a constant of proportionality which means that is the same term
[tex]\frac{8}{9}=\frac{16}{17}[/tex]there is not a proportion between both sides menaning that the expression is false.
Let U= {1,2,3,4,5,6,7,8,9,10}, A={2,4,6,8} B={1,2,3,4}, C={5,6,9}
The symbol that looks like an inverted U means interception. The interception of B and C is given by al the elements that B and C share. In order to find it we simply need to writte B and C and find the numbers that are part of both:
[tex]\begin{gathered} B=\mleft\lbrace1,2,3,4\mright\rbrace \\ C=\mleft\lbrace5,6,9\mright\rbrace \end{gathered}[/tex]As you can see there is no nuber that belongs simultaneously to both B and C. This means that the intersection between B and C is an empty set and is represented with the following symbol:
[tex]\varnothing[/tex]So D is the correct option.
Write the linear equation that gives the rule for this table.
x y
3 13
4 14
5 15
6 16
-Describe the expression.Suvolino bolo2 * 5+7(3 + 13)+Which of the following describes(7 in the expression above?A. factor(B, sumC. quotientD. product
Answer
A. factor
Explanation
The given expression is 2 x 5 + 7(3 + 13)
In the expression given, '7' represents a factor because after adding 3 and 13, you would need to multiply it by 7.
Hence, the correct option is:
A. factor
Factor completely the trinomial 10x^2 + 19x + 7
From the problem :
[tex]10x^2+19x+7[/tex]Factor completely :
We need to find the factors of 10 and 7
We have :
10 = 1 x 10
10 = 2 x 5
7 = 1 x 7
We will do trial and error, The sum of the product of the factors must be equal to the middle term which is 19
Let's say for 10 = 1 x 10 and 7 = 1 x 7
(1 x 7) + (1 x 10) = 17 not equal to 19
(7 x 10) + (1 x 1) = 71 not equal to 19
try the other factors of 10.
10 = 2 x 5 and 7 = 1 x 7
(2 x 7) + (5 x 1) = 19 Equal to 19
Now we have the factors, let's arrange in this way :
[tex](O+I)(I+O)[/tex]O will be the outer and I will be the inner.
O is the paired factors of 10 and 7
For O, we have 2 and 7
For I, we have 5 and 1
This will be :
[tex](2x+5)(x+7)[/tex]The answer is (2x + 5)(x + 7)
What is 8 1/3 times 6 2/5
Answer:53.312
Step-by-step explanation: 8.33 x 6.40
John ordered a large three topping pizza for $7.50 and a large 8 topping pizza for $10. Write an equation in slope intercept form to describe the situation.
Explanation
Step 1
[tex]\begin{gathered} \text{large pizza(3 toppings)}\rightarrow7.5 \\ \text{large pizza( }8\text{ toppings)}\rightarrow10 \\ \text{then we have 2 points of the line} \\ (3,7.5) \\ (8,10) \end{gathered}[/tex]Step 2
find the slope
the slope is given by:
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1(3,7.5)
P2(8,10)
replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{10-7.5}{8-3}=\frac{2.5}{5}=0.5 \\ \text{slope}=0.5 \end{gathered}[/tex]Step 3
usin P1 (3,7.5) ans m= 0.5 find the equation
[tex]\begin{gathered} y-y_1=m(x-x_0) \\ \text{replace} \\ y-7.5=0.5(x-3) \\ y-7.5=0.5x-1.5 \\ y=0.5x-1.5+7.5 \\ y=0.5x+6 \end{gathered}[/tex]I hope this helps you
cual es el valor absoluto de -x+2
The absolute value of -x+2 is 2-|x-2|.
What is the Absolute Value ?
The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|.
Since the absolute value is isolated, we set it equal to the positive and negative of the constant
Therefore,
|(-x+2)| =
for x < 2, -(-x + 2)
for x ≥ 2, (x + 2)
Hence, This is so that no matter the value of x, the value of the function is always greater or equal to 0.
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In the diagram below, <2 = 92o. Determine the measure of all the angles.
**Type in just the numerical answer: Example: 25o you would type just 25
[tex]\angle 1=88^{\circ}[/tex] (linear pair)
[tex]\angle 3=92^{\circ}[/tex] (vertical angles)
[tex]\angle 4=88^{\circ}[/tex] (linear pair)
[tex]\angle 5=88^{\circ}[/tex] (corresponding angles)
[tex]\angle 6=92^{\circ}[/tex] (corresponding angles)
[tex]\angle 7=92^{\circ}[/tex] (linear pair)
[tex]\angle 8=88^{\circ}[/tex] (linear pair)
What is the product of 4 1/5 * 5 ³/7? 22 4/5 20 3/35 20 31/35 22
4x = -3x - 7 need help
Solve the equation for x, solve the operations between similar terms.
[tex]\begin{gathered} 4x=-3x-7 \\ 4x+3x=-7 \\ 7x=-7 \\ x=-\frac{7}{7} \\ x=-1 \end{gathered}[/tex]x has a value of -1.
Plea helpppppp asap, Ik This is easy for you guys but yeah I’m just stupiad
Answer:
Figure 3
Step-by-step explanation:
That is a trapezoid, not a parallelogram.
Which describes the pedestrian crossing sign shown?
The sign is a trapezoid because exactly one pair of opposite sides is parallel.
The sign is a parallelogram because both pairs of opposite sides are parallel.
The sign is a kite because both pairs of opposite sides are congruent.
The sign is a parallelogram because at least one pair of opposite sides is parallel
The sign is a parallelogram because both the pairs of the opposite sides are parallel.
A parallelogram is a quadrilateral with two sets of parallel sides. A parallelogram has opposing sides that are the same length and angles that are the same size. the internal angles on the same side that are in addition to the transversal. The sum of all interior angles is 360 degrees.
Characteristics of a parallelogram:
The contrasting sides are parallel and congruent.Angles that diverge line up.The following angles act as a fallback.If any one of the angles is a right angle, then all the angles will be at right angles.Split in half are the two diagonals.Each diagonal divides the parallelogram into two equal and congruent triangles.A parallelogram's diagonals are equal to the sum of its squares.To learn more about parallelogram visit :
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Answer:
B
Step-by-step explanation:
help pls asap!!Suppose that R and S are points on the number line.
If RS= 8 and S lies at 15, where could R be located?
If there is more than one location, separate them with commas.
Location(s) of R :
Answer:
7, 23
Step-by-step explanation:
R could lie either to the left of S or to the right of S on the number line
Therefore possible values for R are 15-8 = 7
and 15 + 8 = 23
Ms. U.S. Bonds invested a total of $4500, some at 9% per year and the rest at 6% per year. The return for the 9% investment exceeds that from the 6% investment by $180. How much did she Invest at each rate
Using simple interest, the amounts she invested are given as follows:
$3,000 at 9%.$1,500 at 6%.Simple InterestSimple interest is used when there is a single compounding per time period, usually measured in years.
The amount of money after t periods in is modeled by:
A(t) = P(1 + rt)
The interest accrued after t periods is modeled by:
I(t) = Prt
In which:
P is the initial amount.r is the interest rate, as a decimal.She had two investments, investing a total of $4500, hence:
[tex]P_1 + P_2 = 4500[/tex]
The return for the 9% investment exceeds that from the 6% investment by $180, hence:
[tex]I_2 = 0.06(4500 - P_1)[/tex][tex]I_1 = 0.09P_1[/tex][tex]I_2 = I_1 - 180[/tex]Then:
[tex]I_2 = 0.06(4500 - P_1)[/tex]
[tex]I_1 - 180 = 0.06(4500 - P_1)[/tex]
[tex]0.09P_1 - 180 = 0.06(4500 - P_1)[/tex]
[tex]0.15P_1 = 450[/tex]
[tex]P_1 = \frac{450}{0.15}[/tex]
[tex]P_1 = 3000[/tex]
Which is the amount invested at 9%, hence the amount invested at 6%, considering that a total of $4,500 was invested, is given by:
4500 - 3000 = $1,500.
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what is the solution to the equation below? (round your answer to two decimal places.) 6•inx=9.1
ANSWER
B. x = 4.56
EXPLANATION
To solve this equation, first, we have to divide both sides by 6,
[tex]\begin{gathered} \frac{6\cdot\ln x}{6}=\frac{9.1}{6} \\ \\ \ln x=\frac{9.1}{6} \end{gathered}[/tex]Then apply the base exponent rule of logarithms,
[tex]a^{\log_ab}=b[/tex]So, in this case, we have to raise e to each side of the equation,
[tex]\begin{gathered} e^{\ln x}=e^{9.1/6} \\ \\ x\approx4.56 \end{gathered}[/tex]Hence, the solution is x = 4.56, rounded to two decimal places.
Help please this one is tricky
B; False
Here, we want to establish if there is a relationship between two variables
From the question, it was stated that at higher speeds, the ticket fee to be paid will be higher
So, what this mean is that the amount of ticket fee to be paid is a factor of the speed at which she was traveling
This directly makes the speed the independent variable while the ticket fee (value depends on the speed of travel) represents the dependent variable
Hence, we can establish that that the ticekt fee is a function of the speed and not the other way round
This makes the correct option FALSE
Find h (-4), h (0), and h (1).
Answer:
The piecewise function is given below as
[tex]h(x)=\begin{cases}\frac{1}{2}x-2,x<-2 \\ (x-1)^2-1.-2\leq x\leq1 \\ 2,x>1\end{cases}[/tex]Step 1:
To figure out h(-4),
The function that satisfies this is given below as
[tex]\begin{gathered} \frac{1}{2}x-2,x<-2 \\ \text{note:} \\ -4<-2 \end{gathered}[/tex]Therefore,
Substitute the value of x=-4
[tex]\begin{gathered} \frac{1}{2}x-2 \\ h(-4)=\frac{1}{2}(-4)-2 \\ h(-4)=-2-2 \\ h(-4)=-4 \end{gathered}[/tex]Hence,
h( -4 ) = -4
Step 2:
To figure out h(0)
The function that satisfies this condition is given below as
[tex]\begin{gathered} (x-1)^2-1.-2\leq x\leq1 \\ \text{note:} \\ 0<1 \end{gathered}[/tex]Hence,
Substitue the value of x = 0
[tex]\begin{gathered} (x-1)^2-1.-2\leq x\leq1 \\ h(0)=(0-1)^2-1 \\ h(0)=(-1)^2-1 \\ h(0)=1-1 \\ h(0)=0 \end{gathered}[/tex]Hence,
The value for h( 0 ) = 0
Step 3:
To figure out h( 1)
The function that satisfies this condition is given below as
[tex](x-1)^2-1.-2\leq x\leq1[/tex]Substitute x= 1 in the equation below
[tex]\begin{gathered} (x-1)^2-1.-2\leq x\leq1 \\ h(1)=(1-1)^2-1 \\ h(1)=0-1 \\ h(1)=-1 \end{gathered}[/tex]Hence,
The value of h(1) = -1
Solve the following proportion for y.y/5 = 7/8Round your answer to the nearest tenth.
The given proportion is expressed as
y/5 = 7/8
If we crossmultiply, it becomes
y * 8 = 7 * 5
8y = 35
y = 35/8
y = 4.375
Rounding to the nearest tenth,
y = 4.4
What is this number in standard form?
(5 × 1, 000) + (7 × 10) + (8 × 1) + (4 × ) + (1 × 1.000)
16,518
(or 1.6518 x 10⁴)
3. The area of a triangle, in square units,
can be found by multiplying 0.5 times
the length of the base times the height.
A triangle has a base length of 5 meters
and height of 2.6 meters. What is the
area of the triangle?
Answer:
6.5
Step-by-step explanation:
A=hxb
CAN SOMEONE HELP ME PLS
The quotient of the fractions is -5/12
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the fraction expression?The fraction expression is given as
-2 1/2 ÷ 6
Express the mixed number -2 1/2 as an improper fraction
So, we have
-2 1/2 ÷ 6 = -5/2 ÷ 6
Express the division as a product expression
So, we have
-2 1/2 ÷ 6 = -5/2 x 1/6
Evaluate the products
So, we have
-2 1/2 ÷ 6 = -5/12
Hence, the value of the expression is -5/12
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