Write the compound statement "If the food is not good, I won't eat too much" in symbols. Then, construct a truth table for the symbolic statement.r = "The food is good"p = "I eat too much"
Answers
We see that the prase is compounded by the negation of r and q (~r and ~q), and with the following structure:
If the food is not good, I won't eat too much
If ~r then ~p
Represented symbolically as:
~r -> ~p
We can build the truth table:
r p ~r ~p ~r->~p
T T F F T
T F F T T
F T T F F
F F T T T
This, recalling that in the conditional (->), the statement is false only when the first part is true and the second false.
Then, the correct answer is option A.
Related Questions
write the equation of the line in fully simplified intercept form.
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We have the following:
The equation in its slope-intercept form is as follows:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is y-intercept} \end{gathered}[/tex]we calculate the slope like this
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]replacing the points (-8,11) and (10, 2)
[tex]m=\frac{2-11}{10-)-8)}=\frac{-9}{10+8}=\frac{-9}{18}=-\frac{1}{2}[/tex]In this case the y-intercept can be seen in the graph y is (0,7), therefore the value of b is 7
Therefore, the equation would be:
[tex]y=-\frac{1}{2}x+7[/tex]Find the unit rate if it costs $2.48 for 10 slices
Answers
10 slices costs $2.48
The unit rate will be the cost of 1 slice.
Therefore:
[tex]\begin{gathered} \text{Unit Rate}=\frac{\$2.48}{10\text{ Slices}} \\ =\$0.248\text{ per slice} \end{gathered}[/tex]To the nearest cent, the unit rate will be:
$0.25 per slice.
fraction worksheet 6/7 = -----/56
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The missing number is 48
Explanation:Let the missing number be x, then
x/6 = 56/7
x/6 = 8
x = 8 * 6
= 48
i need to fine the common denominator and the answer
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To find the common denominators
In AGHI, the measure of angle I=90^ °, HI = 1.1 feet , and IG = 7.5 feet. Find the measure of angle G to the nearest tenth of a degree.
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To find angle x we can use the tangent function. Remember that the tangent function is defined as:
[tex]\tan \theta=\frac{\text{opp}}{\text{adj}}[/tex]For angle x the opposite leg is 1.1 and the adjacent leg is 7.5, plugging this values into the equation above and solving for x we have:
[tex]\begin{gathered} \tan x=\frac{1.1}{7.5} \\ x=\tan ^{-1}(\frac{1.1}{7.5}) \\ x=8.3 \end{gathered}[/tex]Therefore x is equal to 8.3°
Consumer Math TestYou borrow $13,000 to buy a car. You borrow the money for 4 years and the interest rate is 2.5%. How much interest will you pay? And what is the final price of the car?
Answers
Answer:
You will pay $1,300 in interest.
The final price of the car is of $14,300
Step-by-step explanation:
Simple interest formula:
[tex]I=P\ast r\ast t[/tex]In which:
I is the interest
P is the principal(initial value of the investment, amount borrowed,...)
r is the interest rate, as a decimal
t is the time, in years.
In this question:
Borrow $13,000, so P = 13000
4 years, so t = 4
Interest rate of 2.5%, so r = 0.025
[tex]I=13000\ast0.025\ast4=1300[/tex]You will pay $1,300 in interest.
Final price of the car:
Principal plus interest.
[tex]T=P+I=13000+1300=14300[/tex]The final price of the car is of $14,300
Lizzy is tiling a kitchen floor for the first time. She had a tough time at first and placed only 1 tile the firstday. She started to go faster and by the end of day 4, she had placed 31 tiles. She worked at a steady rate after the first day. Use an equation in point-slope form to determine how many days Lizzy took to place all of the 100 tiles needed to finish the floor. Solve the problem using an equation in point-slope form.Lizzy took______days to place all the tiles. Ok so I was working on this and I have y-1=10(x-1) is this correct so far and what do I do next?
Answers
Answer:
Equation: y - 1 = 10( x - 1)
Explanation:
If we call x the number of days and y the number of tiles placed, then the word problem gives us two points that lie on the line we are trying to find the equation for. These points are (1,1) and (4, 31).
First, we find the slope of the line. The slope is found by dividing the difference in y coordinates by the difference in x -coordinates.
[tex]m=\frac{31-1}{4-1}=\frac{30}{3}[/tex][tex]\boxed{m=3.}[/tex]With the value of the slope in hand, we now use the point (1,1) to write the point-slope equation of the line.
[tex]\boxed{y-1=10\mleft(x-1\mright)_{}}[/tex]With this equation in hand, now let us find how many days it will take Lizzy to place 100 tiles. To find out we substitute y = 100 into the above equation and solve for x.
[tex]100-1=10(x-1)[/tex][tex]\Rightarrow99=10(x-1)[/tex]dividing both sides by 10 gives
[tex]9.9=x-1[/tex]finally, adding 1 to both sides gives
[tex]x=9.9+1[/tex][tex]\boxed{x=10.9.}[/tex]which is about 11 days.
Hence, it took lizzy exactly 10.9 days to place all the tiles.
Factor completely.50u^2 - 18
Answers
Given:
[tex]50u^2-18[/tex]To factor the given equation completely, we factor out common term 2 first:
[tex]2(25u^2-9)[/tex]We can also rewrite this into:
[tex]2((5u)^2-3^2)[/tex]For (5u)^2-3^2, we apply Difference of Two Squares Formula:
[tex]x^2-y^2=(x+y)(x-y)[/tex]where:
x=5u
y=3
So,
[tex](5u)^2-3^2=(5u+3)(5u-3)[/tex]Therefore, the answer is:
[tex]2(5u+3)(5u-3)[/tex]-2 -6-5-4-3-2-1 + 71 2 3 4 5 6 7 8 9 -2 A If this is the graph of f(x) = a*+h nk + k, then: O A. 0 1 O c. ao O a Da > 1
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For the graph given in the question, we have the function
[tex]f(x)=a^{x+h}+k[/tex]If the given graph is for for the function f(x) the
[tex]a>1[/tex]Therefore, the correct option is D
It says to find the volume of the figure and round to the nearest hundredth where necessary. Please help!
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Solution:
Given:
A frustrum with a rectangular top and base.
To find the volume of the figure, we make the sketch as shown below.
The volume of the frustrum is given by;
[tex]Volume\text{ of frustum}=volume\text{ of big pyramid}-volume\text{ of small pyramid}[/tex]The volume of a pyramid is given by;
[tex]\begin{gathered} V=\frac{1}{3}Ah \\ where; \\ A\text{ is the base area} \\ h\text{ is the height} \end{gathered}[/tex]Hence, we get the heights of both pyramids by similarity;
[tex]\begin{gathered} height\text{ of big pyramid}=25.7+x \\ height\text{ of small pyramid}=x \\ base\text{ of small pyramid}=15 \\ base\text{ of big pyramid}=37 \\ \\ Hence,\text{ by similarity,} \\ \frac{h_1}{b_1}=\frac{h_2}{b_2} \\ \frac{25.7+x}{37}=\frac{x}{15} \\ \\ Cross\text{ multiplying,} \\ 15\left(25.7+x\right)=37\times x \\ 385.5+15x=37x \\ Collecting\text{ the like terms,} \\ 385.5=37x-15x \\ 385.5=22x \\ Dividing\text{ both sides by 22;} \\ \frac{385.5}{22}=x \\ x=17.52cm \\ \\ Thus, \\ he\imaginaryI ght\text{ of b}\imaginaryI\text{g pyram}\imaginaryI\text{d}=25.7+x=25.7+17.52 \\ he\mathrm{i}ght\text{ of b}\mathrm{i}\text{g pyram}\mathrm{i}\text{d}=43.22cm \\ \\ he\mathrm{i}ght\text{ of small pyram}\mathrm{i}\text{d}=x \\ he\mathrm{i}ght\text{ of small pyram}\mathrm{i}\text{d}=17.52cm \end{gathered}[/tex]Hence, the volume of the pyramids is calculated;
[tex]\begin{gathered} V=\frac{1}{3}Ah \\ Volume\text{ of the big pyramid}=\frac{1}{3}\times l\times b\times h \\ Volume\text{ of the big pyramid}=\frac{1}{3}\times37\times20\times43.22=31,982.8cm^3 \\ \\ Volume\text{ of the small pyram}\imaginaryI\text{d}=\frac{1}{3}\times l\times b\times h \\ Volume\text{ of the small pyram}\imaginaryI\text{d}=\frac{1}{3}\times15\times20\times17.52=5256cm^3 \\ \\ \\ Volume\text{ of the figure}=31982.8-5256 \\ Volume\text{ of the figure}=26726.80cm^3 \end{gathered}[/tex]Therefore, the volume of the figure to the nearest hundredth is 26,726.80 cubic centimeters.
Another measure of central tendency for a set of data is called the midrange. The midrange is defined as the value that is halfway between the minimum data value and the maximum data value. That is,midrange = minimum value + maximum value2The midrange is often stated as the average of a set of data in situations in which there are a large amount of data and the data are constantly changing. Many weather reports state the average daily temperature of a city as the midrange of the temperatures achieved during that day. For instance, if the minimum daily temperature of a city was 60° and the maximum daily temperature was 90°, then the midrange of the temperatures is 60° + 90°2 = 75° The following daily temperatures were recorded at three-hour intervals.52°, 64°, 65°, 67°, 76°, 72°, 69°, 59°, 55°Determine the following in degrees.(a) the minimum data value _____°(b) the maximum data value _____°(c) the midrange _____°
Answers
To find measures of central tendency on a data set, we organize all data in increasing order; as follows:
52° 55° 59° 64° 65° 67° 69° 72° 76°
minimun data value: 52°
maximum data value: 76°
midrange: (52° + 76°)/2 = 64°
You might need:The equation of a circle is given below.(x-0.5)² + (y - 3,5)² = 16What is its center?(______)What is its radius?If necessary, round your answer to two decimal places.
Answers
Center = (0.5, 3.5) and radius = 4
Explanation:Given the equation:
[tex](x-0.5)^2+(y-3.5)^2=16[/tex]This may be written as:
[tex](x-0.5)^2+(y-3.5)^2=4^2[/tex]Comparing this with the general form of the equation of a circle:
[tex](x-a)^2+(y-b)^2=r^2[/tex]With the center = (a, b) and radius = r, we have:
Center = (0.5, 3.5) and radius = 4
I need help with this problem Harry made 4 hits in 9 times at-bat. If she keeps the same success level, how many hits should she make in 18 timesat-bat?
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We need to find the expected value, first:
[tex]E(x)=p(x)\cdot n[/tex]Where:
[tex]\begin{gathered} p(x)=\frac{4}{9} \\ n=18 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} E(x)=\frac{4}{9}\cdot18 \\ E(x)=8 \end{gathered}[/tex]Answer:
8 hits
Geometry: Trigonometry What is the length of the hypotenuse in triangle ABC? A. 9B. 8C. 10D. 12
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AB = 8
BC = 6
hypotenuse is:
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ AC^2=8^2+6^2 \\ AC^2=64+36 \\ AC^2=100 \\ AC=\sqrt[]{100}=10 \end{gathered}[/tex]answer: C
May I get some help I just want the answer
Answers
The given park ABCD is in the shape of the square, i.e all teh four sides of the part are equal and the angle made by intersection of two side is 90 degree.
i.e.m AB = BC = CD = DA = 120m
and the angle A = Angle B = Angle C = Angle D = 90°
We need to find the length of the diagonal DB,
The side BCD makes a right angle at angle C
In triangle BCD;
BC = 120, CD = 120 for the side DB
Apply Pythagoras theorem;
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
Hypotenuse² = Base ² + Perpendicular²
Substitute, hypotenuse, = DB, Base CD = 120, Perpendicular BC = 120
Hypotenuse² = Base ² + Perpendicular²
DB² = CD² + BC²
DB² = 120² + 120²
DB² = 14400 + 14400
DB² = 28800
DB = 169.70
Since, 169.70 ~ 170
Therefore, DB = 170m
The length of diagonal is 170m
Answer : B) 170m
Which of the following sets contains only rational numbers?OA. {1,326, 1 20.205, √3}OB. {√3, Zz 20.8, 164}oc. {1,326, ' 20.205, √6y}OD. {1,376, 7, 25.205, √64}
Answers
D
Rational numbers are numbers that can be written as a ratio:
[tex]\frac{a}{b}[/tex]Since we can rewrite {1,376, 7, 25.205, √64} as {1,376, 7, 25.205, 8}
then the only option with only rational numbers is D
The table below shows a student's quiz scores on four quizzes. Scores 16 15 15 13 Find this student's mean quiz score
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We are given the following data set:
[tex]1\text{6 15 15 13}[/tex]We are asked to find the mean value, to do that we need to add them all together and divide the result by the number of digits we have, in this case we have 4 numbers, therefore the mean value is the following
[tex]\operatorname{mean}value\text{ = }\frac{16\text{ +15+15+13}}{4}=\frac{59}{4}=14.75[/tex]The student's mean quiz score is 14.75
.
Thanks and have a great day!
I’m confused about this and the other answer is the 1.7 in the trial one
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The most likely error in the data shown would be the .64 in trial 2 because as you may have noticed on all the data in the table, the amount of growth are all more than 1.
One positive integer is 1 less than twice another. The sum of their squares is 34. Find the integers.
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Let's define the following variable.
x = first integer
y = second integer
If the sum of their squares is 34, then we can form the equation below:
[tex]x^2+y^2=34[/tex]If the other integer, say x, is 1 less than twice the other (y), then we can form this second equation:
[tex]x=2y-1[/tex]From these two equations, we can now solve for the values of x and y.
Here are the steps.
1. Replace the value of "x" in equation 1 using the value in equation 2.
[tex](2y-1)^2+y^2=34[/tex]2. Apply the exponent.
[tex]\begin{gathered} (4y^2-4y+1)+y^2=34 \\ 4y^2-4y+1+y^2=34 \end{gathered}[/tex]3. Rearrange the terms. Subtract 34 on both sides of the equation then, combine similar terms.
[tex]\begin{gathered} 4y^2+y^2-4y+1=34 \\ 4y^2+y^2-4y+1-34=34-34 \\ 5y^2-4y-33=0 \end{gathered}[/tex]In step3, we are able to create a quadratic equation in a standard form that is ax² + bx + c wherein a = 5, b = -4, and c = -33.
To solve for the value of y, we can use the Quadratic formula.
[tex]y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Since we have already determined the values of a, b, and c, let's plug them into the formula above.
[tex]y=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(5)(-33)}_{}}{2(5)}[/tex]Then, solve for y.
[tex]\begin{gathered} y=\frac{4\pm\sqrt[]{16+660}}{10} \\ y=\frac{4\pm\sqrt[]{676}}{10} \\ y=\frac{4\pm26}{10} \end{gathered}[/tex]Separate the plus and minus signs.
[tex]\begin{gathered} y=\frac{4+26}{10}=\frac{30}{10}=3 \\ y=\frac{4-26}{10}=-\frac{22}{10}=-2.2 \end{gathered}[/tex]There are two possible values y but only one is an integer. So, we will use y = 3.
To solve for the other integer x, let's use the second equation plugin y = 3.
[tex]\begin{gathered} x=2y-1 \\ x=2(3)-1 \\ x=6-1 \\ x=5 \end{gathered}[/tex]Therefore, the integers are 5 and 3.
line L is shown in the coordinate plane. which of the following is located on line L
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Given the line L.
As shown the line passes through the points (0, 0) and (4, 5)
So, the slope of the line =
[tex]m=\frac{5-0}{4-0}=\frac{5}{4}[/tex]The equation of the line will be:
[tex]y=\frac{5}{4}x[/tex]We will check which point is located on the line L
As we can see from the equation the ratio of y/x = 5/4
So, we will find the ratio of y/x for the given points
[tex]\begin{gathered} (20,25)\rightarrow\frac{y}{x}=\frac{25}{20}=\frac{5}{4} \\ \\ (22,27)\rightarrow\frac{y}{x}=\frac{27}{22} \\ \\ (15,18)\rightarrow\frac{y}{x}=\frac{18}{15}=\frac{6}{5} \end{gathered}[/tex]From the previous results, the answer will be:
The point that is located on the line is (20, 25)
The following summarizes the number of fiction books read last summer by a sample of 33 students.Number of students 2,7,16,8Number of books read per student 2,3,4,7What is the mean number of books read? Round your answer to the nearest tenth.
Answers
The mean is 4
To find the mean of a data set, we use:
[tex]Mean=\frac{Sum\text{ }of\text{ }values}{Total\text{ }number\text{ }of\text{ }values}[/tex]The values given are:
2, 3, 4, 7
The total number of values are 4. Then:
[tex]Mean=\frac{2+3+4+7}{4}=\frac{16}{4}=4[/tex]5) Solve the following systems of linear equations: (10pts each) Sy=44-7 (use substitution) Ly=-2x+5 i) ii) (2x - 3y=8 (use elimination) 16x+5y = -4
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The given set of equations are:
[tex]\begin{gathered} 2x-3y=8\ldots\text{.}\mathrm{}(1) \\ 6x+5y=-4\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]Multiply equation 1 by 5 and equation 2 by 3, we get,
[tex]\begin{gathered} 5(2x-3y)=8\times5\rightarrow10x-15y=40\ldots\text{.}(3) \\ 3(6x+5y)=3\times(-4)\rightarrow18x+15y=-12\ldots\text{.}(4) \end{gathered}[/tex]Now, add equation 3 and 4, we get,
[tex]\begin{gathered} 10x-15y+18x+15y=40-12 \\ 28x=28 \\ x=1 \end{gathered}[/tex]Therefore, from equation 1, with the value of x, we get,
[tex]\begin{gathered} 2-3y=8 \\ 2-8=3y \\ -6=3y \\ y=-\frac{6}{3}=-2 \end{gathered}[/tex]Thus, the solution is, x = 1 and y = -2
Find the equation of the line with the points (-3,-1) and (-4,-7). White the equation in slope intercept from
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To find the equation of the line with the points (-3,-1) and (-4,-7)
First find the slope
m = (y2 -y1) / (x2-x1)
Replace
m= (-7-(-1) / (-4-(-3)
m= -6/-1
m = 6
Use the next formula y-y1 = m(x-x1)
y-(-1) = 6 (x-(-3)
y+1 = 6x +18
y = 6x +18 -1
y = 6x + 17, this is the answer is the slope-intercep form
2. Last year, Mr. Leon had a rectangular gardenwith an area of 208 square feet. This year thedimensions of the garden are the size of thedimensions of last year's garden. What is thearea of Mr. Leon's garden this year?A. 104 ft2B. 416 ft2C. 52 ft2D. 208 ft2
Answers
Answer:
C. 52 ft2
Step-by-step explanation:
Rectangle:
Has two dimensions, which are height(h) and base(b).
The area is: A = b*h
In this question:
We have that that A = b*h = 208.
New dimensions:
Both the dimensions are half(1/2) of last year.
So
A = (b/2)*(h/2) = (b*h)/4
Since b*h = 208
A = (b*h)/4 = 208/4 = 52
Which inequality is equivalent to the following? 5 x/2+ 3 < 12
Answers
We can isolate x to find an equivalent inequality:
[tex]\begin{gathered} \frac{5}{2}\cdot x+3<12 \\ \frac{5}{2}\cdot x<12-3 \\ x<9\cdot\frac{2}{5} \\ x<\frac{18}{5} \end{gathered}[/tex][tex] \frac{2}{n } = \frac{2}{3} \: \\ \\ \\ \: \: a \: deh \\ [/tex]A. n= 30B. n= 3\4C. n=3D. n=1 1/3
Answers
Answer:
The solution is;
[tex]n=3[/tex]Explanation:
Given the equation;
[tex]\frac{2}{n}=\frac{2}{3}[/tex]We want to solve for n;
Let us cross multiply;
[tex]\begin{gathered} \frac{2}{n}=\frac{2}{3} \\ n(2)=2(3) \\ 2n=6 \\ \text{divide both sides by 2;} \\ \frac{2n}{2}=\frac{6}{2} \\ n=3 \end{gathered}[/tex]Therefore, the solution is;
[tex]n=3[/tex]Select all the expressions that are equivalent to 797(–
5).
Answers
The expressions that are equivalent to 797(–5) include the expressions that his a value of -3985.
What is an expression?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case you will multiply the values. This will be:
= 797 × (-5)
= -3985
Therefore, the values given must so he equal to -3985.
Note that an overview was given as the options aren't given.
Learn more expressions on:
brainly.com/question/723406
#SPJ1
What is the radius of a sectorwhen 0== 3/8 radians and thearea is 75/16 sq units?
Answers
The area of a sector of the circle is given by:
[tex]A=\frac{r^2\cdot\theta}{2}[/tex]Where:
A = area
r = radius
θ = angle of radians
Substitute the values:
[tex]\frac{75\pi}{16}=\frac{r^2\cdot\frac{3\pi}{8}}{2}[/tex]Simplify:
[tex]\frac{75\pi}{16}=\frac{r^2\cdot3\pi}{16}[/tex]Solve for r:
[tex]\begin{gathered} \frac{75\pi}{16}\cdot\frac{16}{3\pi}=\frac{r^2\cdot3\pi}{16}\cdot\frac{16}{3\pi} \\ 25=r^2 \\ r=\sqrt{25} \\ r=5 \end{gathered}[/tex]Answer: r = 5 units
On a number line what is the distance between -42.7 and -3.8
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solution
to find the distance, we use subtract. This is:
[tex]undefined[/tex]Use the slope-intercept form to graph the equation y=2/9x+3
Answers
we are given the following equation of a line
[tex]y=\frac{2}{9}x+3[/tex]This is written in the slope-intercept form, which means it follows the general form:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the intercept. We are asked to find the graph, to do that, we can begin by using the intercept since that is the point where the line touches the y-axis, this means that it represents the point (0,b), in our case, this is: (0,3).
Now we need to find a second point, we can use the point where the line touches the x-axis, that is, the point where y = 0, so we set y = 0 in the equation for the line and solve for "x", like this:
[tex]\begin{gathered} y=\frac{2}{9}x+3 \\ 0=\frac{2}{9}x+3 \end{gathered}[/tex]subtracting 3 on both sides
[tex]-3=\frac{2}{9}x[/tex]multipliying by 9 on both sides
[tex]-3(9)=2x[/tex]Dividing by 2 on both sides
[tex]\begin{gathered} \frac{-3(9)}{2}=x \\ -\frac{27}{2}=x \end{gathered}[/tex]therefore, the second point is (-27/2,0). Now we plot both points and join them with a line, like this:
Any two points can be use to plot a line, so one could also use a different value for "x", evaluate that value in the equation for the line and get a value for "y". That point, together with the intercept can be use to plot the line.
We could use for example x = -5, if we replace that value in the equation we get.
[tex]y=\frac{2}{9}(-5)+3=\frac{17}{9}[/tex]we get the point (-5,17/9), and the plot would look like this: