Answer:
Step-by-step explanation:
2x^2+4=0
2(x^2+2)=0
x^2+2=0
x^2=-2
x=✓2*i or x=-✓2*i where i=✓-1
Answer:
[tex]\pm\sqrt{2}i[/tex]
Step-by-step explanation:
[tex]2x^2+9-5=0\\x^2-2=0\\x^2=-2\\x=\pm\sqrt{2}i[/tex]
Done!
What are
are the types of algebric
expression?
Answer:
Step-by-step explanation:
monomial, polynomial, binomial, trinomial and multinomial are the different types of algebraic expressions.
plz mark as brainliest!!!!!!!
Asmaa is shopping for an infant car seat. She has a coupon for 20% off any purchase over $35
at a baby supply store in Manhattan. On a tax-free weekend, she finds a car seat priced at $130.
How much money does Asmaa's coupon save her?
Answer:
just find the persentage on a tax, then minus the orignal price.
Step-by-step explanation:
Answer:
$26
Step-by-step explanation:
thats 20% of 130
If the graph of the function y = f(x) is compressed horizontally by 3, and then reflected across the y -axis , then the resulting graph is the graph of the function :
(a) y = -f(3x) (b) y = f(-3x) (c)y=-f(1/3x)
(d) y = -f(1/3x)
(e) none
Answer:
Please check if the answer is correct or not....
A triangle and a horizontal line are shown. If the triangle is revolved about the horizontal line, what is the resulting object? a triangle next to a horizontal line solid cylinder hollow cylinder solid cone hollow cone with truncated top
Answer:
d. solid cone
Step-by-step explanation:
Solid revolution is the general method used for revolving a given figure about a reference plane to produce a required solid. This process involves the generation of a 3 dimensional shape from a 2 dimensional figure.
A triangle is a three sided figure which generates a solid or hollow cone when it revolves about a given line. If the given triangle is made to revolve about the line, the resulting object would be a solid cone.
Answer:
the answer would be a solid cone
Step-by-step explanation:
i took the test and got it right.
BRAINLIEST PLS PLS PLS PLS I RLY NEED IT
Find the measure of ∠2.
Answer:
∠[tex]2=131[/tex]°
Step-by-step explanation:
We know that ∠[tex]4[/tex] is ≅ ∠[tex]1[/tex].
This means that ∠ [tex]1=49[/tex]°
Therefore, [tex]49+49=98[/tex]°
We know that a trapezoid is [tex]360[/tex]°.
To find ∠[tex]2[/tex] ,which is congruent to ∠[tex]3\\[/tex], we will have to subtract [tex]360[/tex]° from [tex]98[/tex]°.
[tex]360-98=262[/tex]°.
Because ∠[tex]2[/tex]≅∠[tex]3[/tex], we will have to divide [tex]262[/tex] by [tex]2[/tex] to see their measurement.
So,
[tex]\frac{262}{2}=131[/tex].
Hence, ∠[tex]2=131[/tex]°.
I really hope this helps:D
-Jazz
How many months dose it take to pay off 160,000 paying 677 a month
160,000 / 677 = 293.88 months
Hope this helps.
[URGENT] (15 points) F(x) is defined by the equation f(x) = 3x^2 + 3x - 7. What effect will multiplying
f(x) by 0.5 have on the graph?
Answer:
Options (B) and (C).
Step-by-step explanation:
When a quadratic function 'f' is multiplied by k,
1). If k > 0, function 'f' will be vertically stretched Or horizontally compressed.
2). If 0 < k < 1, function will be vertically compressed Or horizontally stretched.
Given quadratic function is,
f(x) = 3x² + 3x - 7
This function is multiplied by 0.5.
Since 0 < 0.5 < 1, therefore, the function will be compressed vertically Or stretched horizontally.
Therefore, Options B and C are the correct options.
John has two jobs. For daytime work at a jewelry store he is paid
$15,000 per month, plus a commission. His monthly commission is
normally distributed with mean $10,000 and standard deviation
$2000. At night he works occasionally as a waiter, for which his
monthly income is normally distributed with mean $1,000 and
standard deviation $300. John's income levels from these two
sources are independent of each other. For a given month, what is
the probability that John's commission from the jewelry store is
between $9,000 and $11,000?
Given Information:
John's mean monthly commission = μ = $10,000
Standard deviation of monthly commission = σ = $2,000
Answer:
[tex]P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%[/tex]
The probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
We want to find out the probability that John's commission from the jewelry store is between $9,000 and $11,000?
[tex]P(9,000 < X < 11,000) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(9,000 < X < 11,000) = P( \frac{9,000 - 10,000}{2,000} < Z < \frac{11,000 - 10,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( \frac{-1,000}{2,000} < Z < \frac{1,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( -0.5 < Z < 0.5 )\\\\P(9,000 < X < 11,000) = P( Z < 0.5 ) - P( Z < -0.5 ) \\\\[/tex]
The z-score corresponding to 0.50 is 0.6915
The z-score corresponding to -0.50 is 0.3085
[tex]P(9,000 < X < 11,000) = 0.6915 - 0.3085 \\\\P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%[/tex]
Therefore, the probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.4, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.50 then go for 0.00 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
A 5-ounce container of greek yogurt contains 150 calories. Find the unit rate of calories per ounce
Answer:
Unit rate of calories per ounce will be 30 calories per ounce
Step-by-step explanation:
Weight of the Greek yogurt container = 5 ounce
Calories per container = 150 calories
Since unit rate of calories per ounce = [tex]\frac{\text{Total calories of the container}}{\text{Total weight of yogurt}}[/tex]
By substituting the given values in the formula,
Unit rat of calories per ounce = [tex]\frac{150}{5}[/tex]
= 30
Therefore, unit rate of calories per ounce will be 30 calories per ounce.
if 36a=45/b, then ab=
Answer:
[tex]1.25[/tex]
Step-by-step explanation:
[tex]let \: a = x \: and \: b = y[/tex]
[tex]36x = \frac{45}{y} [/tex]
[tex]36xy = 45[/tex]
[tex]xy = \frac{45}{36} [/tex]
[tex]xy = 1.25[/tex]
[tex]therefore \: ab \: is \: 1.25[/tex]
5. Calculate, in terms of it, the total surface
area of a solid cylinder of radius 3cm and
height 4cm
Answer:
131.88 cm²
Step-by-step explanation:
At = 2×Acircle + Arectangle
= 2×π·r² + w×h
w = 2π·r = 2·3.14·3 = 18.84 cm
At = 2·3.14·9cm² + 18.84cm·4cm
= 56.52cm² + 75.36cm²
= 131.88 cm²
Frequency table help
Answer: 1) 21-25
2) III
3) II
4) 8
5) 4
Step-by-step explanation:
Question 1: Which numbers are missing?
The previous interval ends at 20 the following interval starts at 26.
The missing interval is 21 - 25
Question 2: How many tally marks to draw?
The frequency is given as 3, so draw three tally marks: III
Question 3: How many tally marks to draw?
The frequency is given as 2, so draw two tally marks: II
Question 4: What is the frequency?
There are eight tally marks so the frequency is 8.
Question 5: What is the frequency?
There are four tally marks so the frequency is 4.
What is the inverse of 520/2 = 260?
260/520 = .5
260 * 2 = 520
2/520 = .004
260 * 520 = 135,200
Answer:
The answer is 260 * 2 = 520
Step-by-step explanation:
520/2 = 260
Multiply both sides by 2
We have
260 × 2 = 560
Hope this helps
Write two point-slope equations for the line passing through the points (6, 5) and (3, 1). Show your work.
Answer:
y=-4/3x-3
Step-by-step explanation:
You look for the slope using the the slope formula (m=y2-y1/x2-x1)
You will end up with (m=1-5/3-6)
Simplify to end up with (-4/3) as your slope.
Then, pick a coordinate point. Your choices are (6,5) and (3,1). You will us it to plug into the equation.
I am picking (3,1) The y-value here is 1 and the x-value is 3.
Your equation to find b, or the y-intercept is going to be (1=-4/3(3)+b)
You will have to simplify.
1=-4/3(3)+b
You will multiply -4/3 and -3 and end up with 4 so it looks like...
1=4+b
You subtract 4 on both sides and then end up with....
-3=b
So, the final answer is: y=-4/3x-3
[tex]\frac{8-i}{3-2i}[/tex] If the expression above is rewritten in the form a+bi, where a and b are real numbers, what is the value of a? (Note: [tex]i=\sqrt{-1}[/tex]
Answer:
a = 2 , b = 1
Step-by-step explanation:
[tex]\frac{8-i}{3-2i}*\frac{3+2i}{3+2i}[/tex]
=> [tex]\frac{(8-i)(3+2i)}{9+4}[/tex]
=> [tex]\frac{24+13i-2i^2}{13}[/tex]
=> [tex]\frac{26+13i}{13}[/tex]
Comparing it with a+bi
a = 26/13 , b = 13/13
a = 2, b = 1
Answer:
a = 2
b = 1
Step-by-step explanation:
[tex]\frac{8-i}{3-2i}[/tex]
Write the fraction in this form:
[tex]\frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}[/tex]
[tex]\frac{\left(8(3)+-1(-2)\right)+\left(-1(3)-8(-2)\right)i}{3^2+-2^2}[/tex]
Evaluate.
[tex]\frac{26+13i}{13}[/tex]
Factor the numerator.
[tex]\frac{13\left(2+i\right)}{13}[/tex]
[tex]2+1i[/tex]
A retail store sells two types of shoes, sneakers and sandals. The store owner pays $8 for the sneakers and $14 for the sandals. The sneakers can be sold for $10 and the sandals can be sold for $17. The owner of the store estimates that she won't sell more than 200 shoes each month, and doesn't plan to invest more that $2,000 on inventory of the shoes. Let x= the number of sneakers in stock, and y=the number of sandals in stock. Write an inequality that represents the possible amount of shoes she can purchase each month. Also, write an inequality that represents how many sneakers and sandals she has in stock each month.
Answer:
The inequality are 8x + 14y ≤ 2000 and x + y ≤ 200
Step-by-step explanation:
The sneaker’s cost = $8
Selling price of sneaker = $10
Cost of sandals = $14
Selling price of sandals = $17
Let the sneaker is x and sandals are y. It is given that total spending amount will not exceed $2000. So the inequality is:
8x + 14y ≤ 2000
since it is given that total number of x and y will not exceed 200 so the inequality that shows number of shoes purchased each year is:
x + y ≤ 200
Which statement is correct regarding g(x) = 35x + 6 - 8 and the parent function f(x) = x ?
O The domains of g(x) and f(x) are the same, but their ranges are not the same.
O The ranges of g(x) and f(x) are the same, but their domains are not the same.
The ranges of g(x) and f(x) are the same, and their domains are also the same.
O The domains of g(x) and f(x) are the not the same, and their ranges are also not the same.
Answer:
The ranges of g(x) and f(x) are the same and their domains are also the same.
Step-by-step explanation:
The function g(x) is the function f(x) multiplied by 35 and later translated twice, first 6 units up and later 8 units down. Since, both expressions are linear functions, both are continuous and both have the same domains and range due to constant slope.
Hence, the ranges of g(x) and f(x) are the same and their domains are also the same.
Marissa has a photograph that measures 2 in. by 4 in. She has mounted the picture on a mat so that there is a border that measures 1 in. around the picture. The graph shows a representation of the photograph and the mat on the coordinate grid. Marissa has decided to dilate the picture and the mat by a scale factor of 2. Draw the new image for the picture and mat on the coordinate grid.
Step-by-step explanation:
The initial image of the photo is 2 in by 4 in. The mat is 4 in by 6 in.
The new image is dilated by a scale of 2. So we double the dimensions. The new photo is 4 in by 8 in. The new mat is 8 in by 12 in.
The new size of the picture is [tex]4\times 8[/tex]and the new size of the mat is [tex]6\times8[/tex]This is shown in attached images.
Given-
The size of the photograph is 2 by 4 in.
Marissa's photograph original size is 2 by 4 in. This is shown in the graph with image one.The boundary required for the mat is 1 in after the photograph applied. Thus the length of the mat must be 3 by 5 in. Refer Image two.When Marissa decided to the picture by the scale factor two she need to multiply its dimension with two.Thus the new dimension of the Picture is,
[tex]=2\times(2,4)[/tex]
[tex]=(4,8)[/tex]
Hence the new size for the picture is 4 by 8 in. This is shown in graph in image three.When Marissa decided to dilate the mat by the scale factor two she need to multiply its dimension with two.Thus the new dimension of the mat is,
[tex]=2\times(3,5)[/tex]
[tex]=(6,10)[/tex]
Hence the new size for the mat is 6 by 10 in. This is shown in graph in image four.Hence the new size of the picture is 4 by 8 and the new size of the mat is 6 by 10. This is shown in attached images.
For more about the scaling the graph follow the link below-
https://brainly.com/question/13819784
A 20-oz iced tea at a certain restaurant has 90 calories. How many calories are there in a 36-oz iced tea?
The 36-oz iced tea has
calories.
Answer:
the answer is 230 calories :)
Step-by-step explanation:
divide 160 by 16 to find out how much 1-oz is then times it by 23 to get the amount of calories in 23-oz. There you go I hope it helps :)
In a random sample of cars driven at low altitudes, of them exceeded a standard of grams of particulate pollution per gallon of fuel consumed. In an independent random sample of cars driven at high altitudes, of them exceeded the standard. Can you conclude that the proportion of high-altitude vehicles exceeding the standard is less than the proportion of low-altitude vehicles exceeding the standard
Complete question is;
In a random sample of 370 cars driven at low altitudes, 43 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 80 cars driven at high altitudes, 23 of them exceeded the standard. Can you conclude that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard at an level of significance? Group of answer choices
Answer:
Yes we can conclude that there is enough evidence to support the claim that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard (P-value = 0.00005).
Step-by-step explanation:
This is a hypothesis test for the difference between the proportions.
The claim is that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.
Then, the null and alternative hypothesis are:
H0 ; π1 - π2 = 0
H1 ; π1 - π2 < 0
The significance level would be established in 0.01.
The random sample 1 (low altitudes), of size n1 = 370 has a proportion of;
p1 = x1/n1
p1 = 43/370
p1 = 0.116
The random sample 2 (high altitudes), of size n2 = 80 has a proportion of;
p2 = x2/n2
p2 = 23/80
p2 = 0.288
The difference between proportions is pd = (p1-p2);
pd = p1 - p2 = 0.116 - 0.288
pd = -0.171
The pooled proportion, we need to calculate the standard error, is:
p = (x1 + x2)/(n1 + n2)
p = (43 + 23)/(370 + 80)
p = 66/450
p = 0.147
The estimated standard error of the difference between means is computed using the formula:
S_(p1-p2) = √[((p(1 - p)/n1) + ((p(1 - p)/n2)]
1 - p = 1 - 0.147 = 0.853
Thus;
S_(p1-p2) = √[((0.147 × 0.853)/370) + ((0.147 × 0.853)/80)]
S_(p1-p2) = 0.044
Now, we can use the formula for z-statistics as;
z = (pd - (π1 - π2))/S_(p1-p2)
z = (-0.171 - 0)/0.044
z = -3.89
Using z-distribution table, we have the p-value = 0.00005
Since the P-value of (0.00005) is smaller than the significance level (0.01), then the effect is significant.
We conclude that The null hypothesis is rejected.
Thus, there is enough evidence to support the claim that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.
EXPONENTIAL FUNCTIONS HELP Write the function for each graph described below. the graph of f(x) = 2x reflected across the x-axis. The graph of f(x)= 1/3x translated up 5 units. The graph of f(x) = 3x left 2 units, and down 3. The graph of f(x) = 1/2x translated down 2 units. The graph of f(x) = 4x stretched horizontally by a factor of 3. The graph of f(x) = 2x up 4 units, right 3.
Answer:
-2^x(1/3)^x +53^(x +2) -3(1/2)^x -24^(x/3)2^(x -3) +4Step-by-step explanation:
In general, the transformation ...
g(x) = f(x -h) +k
translates f(x) right h units and up k units.
The transformation ...
g(x) = f(x/a)
stretches the graph horizontally by a factor of "a".
The transformation ...
g(x) = -f(x)
causes the graph to be reflected over the x-axis.
___
Applying the above, we have ...
f(x) = 2^x reflected over x is g(x) = -2^x
f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5
f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3
f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2
f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)
f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4
Answer:
-2^x
(1/3)^x +5
3^(x +2) -3
(1/2)^x -2
4^(x/3)
2^(x -3) +4
Step-by-step explanation:
In general, the transformation ...
g(x) = f(x -h) +k
translates f(x) right h units and up k units.
The transformation ...
g(x) = f(x/a)
stretches the graph horizontally by a factor of "a".
The transformation ...
g(x) = -f(x)
causes the graph to be reflected over the x-axis.
___
Applying the above, we have ...
f(x) = 2^x reflected over x is g(x) = -2^x
f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5
f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3
f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2
f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)
f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4
Find the slope of the line shown on the graph to the right.
Select the correct choice below and fill in any answer boxes within your choice.
#
A. The slope of the line is
(Simplify your answer. Type an integer or a fraction.)
B. The slope is undefined
Answer:
0 (zero)
Step-by-step explanation:
A horizontal line has zero slope.
Find the side of a cube with surface area of 150cm square
Anyone that answers my question I will mark as brilliant
Answer:
5cm for each side
Answer:
5 cmsolution,
Surface area= 150 cm^2
Side of a cube(a)=?
Now,
[tex]surface \: area \: of \: cube = 6 {a}^{2} \\ or \: 150 = 6 {a}^{2} \\ or \: {a}^{2} = \frac{150}{6} \\ or \: {a}^{2} = 25 \\ or \: a = \sqrt{25} \\ or \: a = \sqrt{ {(5)}^{2} } \\ a = 5 \: cm[/tex]
Hope this helps...
Good luck on your assignment..
You walk around a circular pond of radius 13 miles for angle of theta = 10 degrees degree Which one of the following shows the distance you walked around the pond? (Take pi approx 3.14)
(A) 0.27 miles
(B) 10 miles
(C) 2.27 miles
(D) 1.3 miles
Answer:
(C) 2.27 miles
Step-by-step explanation:
Without doing any detailed calculation, you can estimate the distance. The angle of 10° is 1/36 of the full circle of 360°. The circumference is given by the formula ...
C = 2πr = 2(3.14)(13)
We want to find 1/36 of that circumference, which will be about ...
C/36 = (3.14)(2)(13)/36 ≈ 3.14(2/3) ≈ 2
This is sufficiently accurate to determine that the best choice is (C).
__
If you want to use a calculator, you can figure the distance as ...
C/36 = (3.14)(26/36) ≈ 2.26777...(repeating) ≈ 2.27 . . . miles
Find the position function of a particle moving along a coordinate line that satisfies the given conditions. 2sint-cost
Answer:
the position of a particle moving at a coordinate say(y) will satisfy the given conditions t=0 (say) if y=2sint-cost
Step-by-step explanation:
Clearly by the above we can see that if y=2sint-cost at t=0, then y=-1 because at t=0 sint vanishes and leaves us with only cost and at t=0 cos0=1
Two cars start moving from the same point. One travels south at 16 mi/h and the other travels west at 12 mi/h. At what rate is the distance between the cars increasing three hours later?
Answer:
20 miles per hour
Step-by-step explanation:
The distances traveled by each car are perpendicular, so we can find the distance between the cars using the Pythagoras' theorem between their distances traveled:
[tex]d^2 = d_1^2 + d_2^2[/tex]
Where d is the distance between the cars, d1 is the distance traveled by the first car and d2 is the distance traveled by the second car.
The distance traveled is calculated by the speed times the time traveled, so we have:
[tex]d^2 = (16t)^2 + (12t)^2[/tex]
[tex]d^2 = 256t^2 + 144t^2[/tex]
[tex]d^2 = 400t^2[/tex]
[tex]d = 20t[/tex]
The rate that the distance is increasing can be found with the derivative of the distance in relation to the time:
[tex]dd/dt = 20\ mph[/tex]
So the rate that the distance increases is always 20 miles per hour, and it's independent of the time.
the expression7(b+3) is equivalent to which expression? A.7b+3, B.7+b+c, C.7b+10, D.7b+21
Answer:
7b+21
Step-by-step explanation:
7(b+3)
Distribute
7*b + 7*3
7b+21
Select all the correct equations.
Which equations have no real solution but have two complex solutions? PLZ 20 POINTS
Answer:
You did not post the options, but i will try to answer this in a general way.
Because we have two solutions, i know that we are talking about quadratic equations, of the form of:
0 = a*x^2 + b*x + c.
There are two easy ways to see if the solutions of this equation are real or not.
1) look at the graph, if the graph touches the x-axis, then we have real solutions (if the graph does not touch the x-axis, we have complex solutions).
2) look at the determinant.
The determinant of a quadratic equation is:
D = b^2 - 4*a*c.
if D > 0, we have two real solutions.
if D = 0, we have one real solution (or two real solutions that are equal)
if D < 0, we have two complex solutions.
Answer:
This was for 5 points. not 20 my dude. Also the first answer is correct.
Step-by-step explanation:
The following table represents a probability distribution for a random variable, X. What must P(5) be?
Answer:
c) 0.1
P(5) = 0.1
Step-by-step explanation:
Given data
x : 0 1 2 3 4 5
p(x): 0.2 0.1 0.3 0.1 0.2 ?
Given data is discrete distribution
if the numbers [tex]P(x_{i} )[/tex] i = 1,2,3..... satisfies the two conditions
i) [tex]P(x_{i} )\geq 0[/tex] for all values of 'i'
ii) ∑P(x) = 1
Given data
i) [tex]P(x_{i} )\geq 0[/tex] for all values of 'i'
ii) ∑P(x) = 1
P(x=1) + P(x=2) +P(x=3) +P(x=4)+P(x=5) =1
⇒ 0.2 + 0.1 + 0.3 +0.1 +0.2 + p(X=5) = 1
⇒ 0.9 +p(5) =1
⇒ p(5) = 1 -0.9
⇒ P(5) = 0.1
Can someone help me with this
Answer:
10
Step-by-step explanation:
Since 75 sandwiches have salad this means that 75 - 30 = 45 of them have tuna with salad. Therefore, the amount of sandwiches that have cheese without salad is 100 - (30 + 15 + 45) = 100 - 90 = 10.